{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T20:53:08Z","timestamp":1768078388742,"version":"3.49.0"},"reference-count":88,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T00:00:00Z","timestamp":1663632000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T00:00:00Z","timestamp":1663632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s10479-022-04970-3","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T11:10:41Z","timestamp":1663672241000},"page":"859-900","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A welcome to the jungle of continuous-time multivariate non-Gaussian models based on L\u00e9vy processes applied to finance"],"prefix":"10.1007","volume":"352","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1865-6935","authenticated-orcid":false,"given":"Michele Leonardo","family":"Bianchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asmerilda","family":"Hitaj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gian Luca","family":"Tassinari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,20]]},"reference":[{"key":"4970_CR1","unstructured":"Allen, D., & Satchell, S. (2014). The four horsemen: Heavy-tails, negative skew, volatility clustering, asymmetric dependence. Discussion Paper, University of Sydney, n. 4."},{"key":"4970_CR2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809781","volume-title":"L\u00e9vy processes and stochastic calculus","author":"D Applebaum","year":"2009","unstructured":"Applebaum, D. (2009). L\u00e9vy processes and stochastic calculus. Cambridge: Cambridge University Press."},{"key":"4970_CR3","doi-asserted-by":"crossref","unstructured":"Arellano-Valle, R. B., & Azzalini, A. (2021) A formulation for continuous mixtures of multivariate normal distributions. Journal of Multivariate Analysis, 185, 104780. https:\/\/doi.org\/10.1016\/j.jmva.2021.104780","DOI":"10.1016\/j.jmva.2021.104780"},{"issue":"13","key":"4970_CR4","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1080\/1351847X.2013.870917","volume":"22","author":"L Ballotta","year":"2016","unstructured":"Ballotta, L., & Bonfiglioli, E. (2016). Multivariate asset models using L\u00e9vy processes and applications. The European Journal of Finance, 22(13), 1320\u20131350.","journal-title":"The European Journal of Finance"},{"issue":"5","key":"4970_CR5","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1017\/S0022109018001321","volume":"54","author":"L Ballotta","year":"2019","unstructured":"Ballotta, L., Fusai, G., Loregian, A., & Perez, M. F. (2019). Estimation of multivariate asset models with jumps. Journal of Financial and Quantitative Analysis, 54(5), 2053\u20132083.","journal-title":"Journal of Financial and Quantitative Analysis"},{"issue":"1674","key":"4970_CR6","first-page":"401","volume":"353","author":"OE Barndorff-Nielsen","year":"1977","unstructured":"Barndorff-Nielsen, O. E. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 353(1674), 401\u2013419.","journal-title":"Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences"},{"issue":"1","key":"4970_CR7","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1017\/S0001867800010685","volume":"33","author":"OE Barndorff-Nielsen","year":"2001","unstructured":"Barndorff-Nielsen, O. E., Pedersen, J., & Sato, K. I. (2001). Multivariate subordination, self-decomposability and stability. Advances in Applied Probability, 33(1), 160\u2013187.","journal-title":"Advances in Applied Probability"},{"issue":"4","key":"4970_CR8","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1016\/j.jbankfin.2009.09.009","volume":"34","author":"M Bedendo","year":"2010","unstructured":"Bedendo, M., Campolongo, F., Joossens, E., & Saita, F. (2010). Pricing multiasset equity options: How relevant is the dependence function? Journal of Banking and Finance, 34(4), 788\u2013801.","journal-title":"Journal of Banking and Finance"},{"key":"4970_CR9","volume-title":"L\u00e9vy processes","author":"J Bertoin","year":"1996","unstructured":"Bertoin, J. (1996). L\u00e9vy processes. Cambridge: Cambridge University Press."},{"key":"4970_CR10","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1080\/14697688.2020.1733057","volume":"20","author":"ML Bianchi","year":"2020","unstructured":"Bianchi, M. L., & Tassinari, G. L. (2020). Forward-looking portfolio selection with multivariate non-Gaussian models. Quantitative Finance, 20, 1645\u20131661.","journal-title":"Quantitative Finance"},{"issue":"1","key":"4970_CR11","first-page":"59","volume":"55","author":"ML Bianchi","year":"2011","unstructured":"Bianchi, M. L., Rachev, S. T., Kim, Y. S., & Fabozzi, F. J. (2011). Tempered infinitely divisible distributions and processes. Theory of Probability and Its Applications (TVP), 55(1), 59\u201386.","journal-title":"Theory of Probability and Its Applications (TVP)"},{"issue":"4","key":"4970_CR12","doi-asserted-by":"crossref","first-page":"1650027","DOI":"10.1142\/S0219024916500278","volume":"19","author":"ML Bianchi","year":"2016","unstructured":"Bianchi, M. L., Tassinari, G. L., & Fabozzi, F. J. (2016). Riding with the four horsemen and the multivariate normal tempered stable model. International Journal of Theoretical and Applied Finance, 19(4), 1650027.","journal-title":"International Journal of Theoretical and Applied Finance"},{"issue":"1","key":"4970_CR13","first-page":"59","volume":"423\u2013445","author":"ML Bianchi","year":"2017","unstructured":"Bianchi, M. L., Rachev, S. T., & Fabozzi, F. J. (2017). Tempered stable Ornstein\u2013Uhlenbeck processes: A practical view. Communications in Statistics - Simulation and Computation, 423\u2013445(1), 59\u201386.","journal-title":"Communications in Statistics - Simulation and Computation"},{"key":"4970_CR14","doi-asserted-by":"crossref","DOI":"10.1142\/11118","volume-title":"Handbook of heavy-tailed distributions in asset management and risk management","author":"ML Bianchi","year":"2019","unstructured":"Bianchi, M. L., Stoyanov, S. V., Tassinari, G. L., Fabozzi, F. J., & Focardi, S. M. (2019). Handbook of heavy-tailed distributions in asset management and risk management. World Scientific."},{"key":"4970_CR15","doi-asserted-by":"crossref","unstructured":"Bianchi,M. L., De Luca, G., & Rivieccio, G. (2022). Non-Gaussian models for CoVaR estimation. International Journal of Forecasting. https:\/\/doi.org\/10.1016\/j.ijforecast.2021.12.002","DOI":"10.1016\/j.ijforecast.2021.12.002"},{"issue":"4","key":"4970_CR16","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1080\/14697688.2018.1523547","volume":"19","author":"L Boen","year":"2019","unstructured":"Boen, L., & Guillaume, F. (2019). Building multivariate Sato models with linear dependence. Quantitative Finance, 19(4), 619\u2013645.","journal-title":"Quantitative Finance"},{"key":"4970_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11147-019-09155-y","volume":"23","author":"L Boen","year":"2019","unstructured":"Boen, L., & Guillaume, F. (2019). Towards a $$\\Delta $$-Gamma Sato multivariate model. Review of Derivatives Research, 23, 1\u201339.","journal-title":"Review of Derivatives Research"},{"key":"4970_CR18","doi-asserted-by":"crossref","DOI":"10.1002\/9781118835364","volume-title":"Advanced equity derivatives: Volatility and correlation","author":"S Bossu","year":"2014","unstructured":"Bossu, S. (2014). Advanced equity derivatives: Volatility and correlation. Wiley."},{"issue":"3","key":"4970_CR19","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1142\/S0219024900000541","volume":"3","author":"SI Boyarchenko","year":"2000","unstructured":"Boyarchenko, S. I., & Levendorskii, S. Z. (2000). Option pricing for truncated L\u00e9vy processes. International Journal of Theoretical and Applied Finance, 3(3), 549\u2013552.","journal-title":"International Journal of Theoretical and Applied Finance"},{"key":"4970_CR20","doi-asserted-by":"crossref","DOI":"10.1142\/4955","volume-title":"Non-Gaussian Merton\u2013Black\u2013Scholes theory","author":"SI Boyarchenko","year":"2002","unstructured":"Boyarchenko, S. I., & Levendorskii, S. Z. (2002). Non-Gaussian Merton\u2013Black\u2013Scholes theory. World Scientific Publishing."},{"issue":"7","key":"4970_CR21","doi-asserted-by":"crossref","first-page":"2208","DOI":"10.1016\/j.spa.2016.10.008","volume":"127","author":"B Buchmann","year":"2017","unstructured":"Buchmann, B., Kaehler, B., Maller, R., & Szimayer, A. (2017). Multivariate subordination using generalised Gamma convolutions with applications to variance gamma processes and option pricing. Stochastic Processes and Their Applications., 127(7), 2208\u20132242.","journal-title":"Stochastic Processes and Their Applications."},{"issue":"4","key":"4970_CR22","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1007\/s11009-018-9655-y","volume":"21","author":"B Buchmann","year":"2019","unstructured":"Buchmann, B., Lu, K. W., & Madan, D. B. (2019). Calibration for weak variance-alpha-gamma processes. Methodology and Computing in Applied Probability, 21(4), 1151\u20131164.","journal-title":"Methodology and Computing in Applied Probability"},{"issue":"11","key":"4970_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v034.i11","volume":"34","author":"P Chauss\u00e9","year":"2010","unstructured":"Chauss\u00e9, P. (2010). Computing generalized method of moments and generalized empirical likelihood with R. Journal of Statistical Software, 34(11), 1\u201335.","journal-title":"Journal of Statistical Software"},{"issue":"1","key":"4970_CR24","doi-asserted-by":"crossref","first-page":"135","DOI":"10.2307\/1913889","volume":"41","author":"PK Clark","year":"1973","unstructured":"Clark, P. K. (1973). A subordinated stochastic process model with finite variance for speculative prices. Econometrica, 41(1), 135\u2013155.","journal-title":"Econometrica"},{"issue":"3","key":"4970_CR25","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0165-1684(94)90029-9","volume":"36","author":"P Comon","year":"1994","unstructured":"Comon, P. (1994). Independent component analysis, a new concept? Signal Processing, 36(3), 287\u2013314.","journal-title":"Signal Processing"},{"key":"4970_CR26","volume-title":"Financial modelling with jump processes","author":"R Cont","year":"2003","unstructured":"Cont, R., & Tankov, P. (2003). Financial modelling with jump processes. Chapman and Hall\/CRC."},{"issue":"1","key":"4970_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 39(1), 1\u201338.","journal-title":"Journal of the Royal Statistical Society. Series B (Methodological)"},{"issue":"1","key":"4970_CR28","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0167-7152(02)00040-8","volume":"57","author":"K Dimitris","year":"2002","unstructured":"Dimitris, K. (2002). An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution. Statistics and Probability Letters, 57(1), 43\u201352.","journal-title":"Statistics and Probability Letters"},{"issue":"4","key":"4970_CR29","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1007\/s00180-012-0384-3","volume":"28","author":"Y Dominicy","year":"2013","unstructured":"Dominicy, Y., Ogata, H., & Veredas, D. (2013). Inference for vast dimensional elliptical distributions. Computational Statistics, 28(4), 1853\u20131880.","journal-title":"Computational Statistics"},{"issue":"3","key":"4970_CR30","doi-asserted-by":"crossref","first-page":"288","DOI":"10.2307\/3318481","volume":"1","author":"E Eberlein","year":"1995","unstructured":"Eberlein, E., & Keller, U. (1995). Hyperbolic distributions in finance. Bernoulli, 1(3), 288\u2013299.","journal-title":"Bernoulli"},{"key":"4970_CR31","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/978-3-662-12429-1_12","volume-title":"Mathematical finance. Bachelier congress","author":"E Eberlein","year":"2002","unstructured":"Eberlein, E., & Prause, K. (2002). The generalized hyperbolic model: Financial derivatives and risk measures. In H. Geman, D. Madan, S. R. Pliska, & T. Vorst (Eds.), Mathematical finance. Bachelier congress (pp. 245\u2013267). Springer."},{"issue":"7","key":"4970_CR32","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1080\/14697688.2015.1111522","volume":"16","author":"HA Fallahgoul","year":"2016","unstructured":"Fallahgoul, H. A., Kim, Y. S., & Fabozzi, F. J. (2016). Elliptical tempered stable distribution. Quantitative Finance, 16(7), 1069\u20131087.","journal-title":"Quantitative Finance"},{"key":"4970_CR33","unstructured":"Frahm, G. (2004). Generalized elliptical distributions: Theory and applications. PhD thesis, Universit\u00e4t zu K\u00f6ln."},{"issue":"1","key":"4970_CR34","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1111\/1467-9965.00108","volume":"11","author":"H Geman","year":"2001","unstructured":"Geman, H., Madan, D., & Yor, M. (2001). Time changes for L\u00e9vy processes. Mathematical Finance, 11(1), 79\u201396.","journal-title":"Mathematical Finance"},{"issue":"1","key":"4970_CR35","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s11147-012-9080-2","volume":"16","author":"F Guillaume","year":"2013","unstructured":"Guillaume, F. (2013). The $$\\alpha $$VG model for multivariate asset pricing: Calibration and extension. Review of Derivatives Research, 16(1), 25\u201352.","journal-title":"Review of Derivatives Research"},{"key":"4970_CR36","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.2307\/1912775","volume":"50","author":"LP Hansen","year":"1982","unstructured":"Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50, 1029\u20131054.","journal-title":"Econometrica"},{"issue":"1","key":"4970_CR37","doi-asserted-by":"crossref","first-page":"39","DOI":"10.2307\/2330989","volume":"21","author":"L Harris","year":"1986","unstructured":"Harris, L. (1986). Cross-security tests of the mixture distribution. Journal of Financial and Quantitative Analysis, 21(1), 39\u201346.","journal-title":"Journal of Financial and Quantitative Analysis"},{"issue":"1","key":"4970_CR38","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s11408-012-0202-5","volume":"27","author":"A Hitaj","year":"2013","unstructured":"Hitaj, A., & Mercuri, L. (2013). Portfolio allocation using multivariate variance gamma models. Financial Markets and Portfolio Management, 27(1), 65\u201399.","journal-title":"Financial Markets and Portfolio Management"},{"key":"4970_CR39","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1057\/9781137025098_14","volume-title":"Advances in financial risk management","author":"A Hitaj","year":"2013","unstructured":"Hitaj, A., & Mercuri, L. (2013). Hedge fund portfolio allocation with higher moments and MVG models. In J. A. Batten, P. MacKay, & N. Wagner (Eds.), Advances in financial risk management (pp. 331\u2013346). Palgrave Macmillan."},{"key":"4970_CR40","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.frl.2015.09.005","volume":"15","author":"A Hitaj","year":"2015","unstructured":"Hitaj, A., Mercuri, L., & Rroji, E. (2015). Portfolio selection with independent component analysis. Finance Research Letters, 15, 146\u2013159.","journal-title":"Finance Research Letters"},{"issue":"3","key":"4970_CR41","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1111\/insr.12265","volume":"86","author":"A Hitaj","year":"2018","unstructured":"Hitaj, A., Hubalek, F., Mercuri, L., & Rroji, E. (2018). On properties of the MixedTS distribution and its multivariate extension. International Statistical Review, 86(3), 512\u2013540.","journal-title":"International Statistical Review"},{"issue":"1\u20132","key":"4970_CR42","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s10287-018-0306-0","volume":"16","author":"A Hitaj","year":"2019","unstructured":"Hitaj, A., Mercuri, L., & Rroji, E. (2019). Sensitivity analysis of the mixed tempered stable parameters with implications in portfolio optimization. Computational Management Science, 16(1\u20132), 71\u201395.","journal-title":"Computational Management Science"},{"key":"4970_CR43","unstructured":"Hu, W. (2005). Calibration Of multivariate generalized hyperbolic distributions using the EM algorithm, with applications in risk management, portfolio optimization and portfolio credit risk. PhD thesis, Florida State University."},{"issue":"4\u20135","key":"4970_CR44","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/S0893-6080(00)00026-5","volume":"13","author":"A Hyv\u00e4rinen","year":"2000","unstructured":"Hyv\u00e4rinen, A., & Erkki, O. (2000). Independent component analysis: Algorithms and applications. Neural Networks, 13(4\u20135), 411\u2013430.","journal-title":"Neural Networks"},{"issue":"2","key":"4970_CR45","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/j.1467-9965.2011.00504.x","volume":"23","author":"VK Kaishev","year":"2013","unstructured":"Kaishev, V. K. (2013). L\u00e9vy processes induced by Dirichlet (b-)splines: Modeling multivariate asset price dynamics. Mathematical Finance, 23(2), 217\u2013247.","journal-title":"Mathematical Finance"},{"issue":"7","key":"4970_CR46","doi-asserted-by":"crossref","first-page":"1551","DOI":"10.1016\/j.jmva.2005.11.001","volume":"97","author":"J Kallsen","year":"2006","unstructured":"Kallsen, J., & Tankov, P. (2006). Characterization of dependence of multidimensional L\u00e9vy processes using L\u00e9vy copulas. Journal of Multivariate Analysis, 97(7), 1551\u20131572.","journal-title":"Journal of Multivariate Analysis"},{"issue":"5","key":"4970_CR47","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1080\/14697680902744729","volume":"9","author":"R Kawai","year":"2009","unstructured":"Kawai, R. (2009). A multivariate L\u00e9vy process model with linear correlation. Quantitative Finance, 9(5), 597\u2013606.","journal-title":"Quantitative Finance"},{"issue":"1","key":"4970_CR48","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s10479-012-1229-8","volume":"201","author":"YS Kim","year":"2012","unstructured":"Kim, Y. S., Giacometti, R., Rachev, S. T., Fabozzi, F. J., & Mignacca, D. (2012). Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model. Annals of Operations Research, 201(1), 325\u2013343.","journal-title":"Annals of Operations Research"},{"key":"4970_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-022-04613-7","author":"YS Kim","year":"2022","unstructured":"Kim, Y. S. (2022). Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-022-04613-7","journal-title":"Annals of Operations Research"},{"key":"4970_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.frl.2021.102143","author":"T Kurosaki","year":"2021","unstructured":"Kurosaki, T., & Kim, Y. S. (2021). Cryptocurrency portfolio optimization with multivariate normal tempered stable process and Foster\u2013Hart risk. Finance Research Letters. https:\/\/doi.org\/10.1016\/j.frl.2021.102143","journal-title":"Finance Research Letters"},{"issue":"2","key":"4970_CR51","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1111\/j.1368-423X.2009.00290.x","volume":"12","author":"S Kring","year":"2009","unstructured":"Kring, S., Rachev, S. T., H\u00f6chst\u00f6tter, M., Fabozzi, F. J., & Bianchi, M. L. (2009). Multi-tail generalized elliptical distributions for asset returns. Econometrics Journal, 12(2), 272\u2013291.","journal-title":"Econometrics Journal"},{"key":"4970_CR52","unstructured":"Leoni, P., & Schoutens, W. (2008). Multivariate smiling. Wilmott magazine, March."},{"issue":"2","key":"4970_CR53","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jeconom.2008.10.007","volume":"148","author":"Q Li","year":"2009","unstructured":"Li, Q., Maasoumi, E., & Racine, S. R. (2009). A nonparametric test for equality of distributions with mixed categorical and continuous data. Journal of Econometrics, 148(2), 186\u2013200.","journal-title":"Journal of Econometrics"},{"issue":"4","key":"4970_CR54","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1093\/biomet\/81.4.633","volume":"81","author":"C Liu","year":"1994","unstructured":"Liu, C., & Rubin, D. B. (1994). The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence. Biometrika, 81(4), 633\u2013648.","journal-title":"Biometrika"},{"issue":"2","key":"4970_CR55","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1093\/rfs\/13.2.257","volume":"13","author":"AW Lo","year":"2000","unstructured":"Lo, A. W., & Wang, J. (2000). Trading volume: Definitions, data analysis, and implications of portfolio theory. Review of Financial Studies, 13(2), 257\u2013300.","journal-title":"Review of Financial Studies"},{"issue":"2","key":"4970_CR56","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.spl.2011.10.004","volume":"82","author":"A Loregian","year":"2012","unstructured":"Loregian, A., Mercuri, L., & Rroji, E. (2012). Approximation of the variance gamma model with a finite mixture of normals. Statistics and Probability Letters, 82(2), 217\u2013224.","journal-title":"Statistics and Probability Letters"},{"issue":"5","key":"4970_CR57","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1080\/14697680600806275","volume":"6","author":"E Luciano","year":"2006","unstructured":"Luciano, E., & Schoutens, W. (2006). A multivariate jump-driven financial asset model. Quantitative Finance, 6(5), 385\u2013402.","journal-title":"Quantitative Finance"},{"issue":"3","key":"4970_CR58","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1142\/S0219024910005838","volume":"13","author":"E Luciano","year":"2010","unstructured":"Luciano, E., & Semeraro, P. (2010). A generalized normal mean\u2013variance mixture for return processes in finance. International Journal of Theoretical and Applied Finance, 13(3), 415\u2013440.","journal-title":"International Journal of Theoretical and Applied Finance"},{"issue":"8","key":"4970_CR59","doi-asserted-by":"crossref","first-page":"1937","DOI":"10.1016\/j.cam.2009.08.119","volume":"233","author":"E Luciano","year":"2010","unstructured":"Luciano, E., & Semeraro, P. (2010). Multivariate time changes for L\u00e9vy asset models: Characterization and calibration. Journal of Computational and Applied Mathematics, 233(8), 1937\u20131953.","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"7","key":"4970_CR60","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1080\/14697688.2015.1114661","volume":"16","author":"E Luciano","year":"2016","unstructured":"Luciano, E., Marena, M., & Semeraro, P. (2016). Dependence calibration and portfolio fit with factor-based subordinators. Quantitative Finance, 16(7), 1037\u20131052.","journal-title":"Quantitative Finance"},{"issue":"1","key":"4970_CR61","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1023\/A:1009703431535","volume":"2","author":"D Madan","year":"1998","unstructured":"Madan, D., Carr, P., & Chang, E. (1998). The variance gamma process and option pricing. Review of Finance, 2(1), 79\u2013105.","journal-title":"Review of Finance"},{"issue":"8","key":"4970_CR62","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1080\/14697688.2017.1420210","volume":"18","author":"DB Madan","year":"2018","unstructured":"Madan, D. B. (2018). Instantaneous portfolio theory. Quantitative Finance, 18(8), 1345\u20131364.","journal-title":"Quantitative Finance"},{"key":"4970_CR63","doi-asserted-by":"crossref","unstructured":"Madan, D. B. & Yen, J.-Y. (2007). Asset allocation with multivariate non-Gaussian returns. In Birge, J. R. & Linetsky, V. (Eds.), Handbook of Financial Engineering (chapter 23). North Holland, Amsterdam. https:\/\/doi.org\/10.1016\/S0927-0507(07)15023-4","DOI":"10.1016\/S0927-0507(07)15023-4"},{"issue":"1","key":"4970_CR64","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1080\/14697688.2010.505199","volume":"12","author":"R Marf\u00e9","year":"2012","unstructured":"Marf\u00e9, R. (2012). A generalized variance gamma process for financial applications. Quantitative Finance, 12(1), 75\u201387.","journal-title":"Quantitative Finance"},{"issue":"04","key":"4970_CR65","doi-asserted-by":"crossref","first-page":"1250028","DOI":"10.1142\/S0219024912500288","volume":"15","author":"R Marf\u00e9","year":"2012","unstructured":"Marf\u00e9, R. (2012). A multivariate pure-jump model with multi-factorial dependence structure. International Journal of Theoretical and Applied Finance, 15(04), 1250028.","journal-title":"International Journal of Theoretical and Applied Finance"},{"key":"4970_CR66","volume-title":"Quantitative risk management: Concepts, techniques, and tools","author":"A McNeil","year":"2005","unstructured":"McNeil, A., Frey, R., & Embrechts, P. (2005). Quantitative risk management: Concepts, techniques, and tools. Princeton University Press."},{"key":"4970_CR67","doi-asserted-by":"crossref","DOI":"10.1002\/9781118809204","volume-title":"Correlation risk modeling and management: An applied guide including the Basel III correlation framework-with interactive models in Excel\/VBA","author":"G Meissner","year":"2014","unstructured":"Meissner, G. (2014). Correlation risk modeling and management: An applied guide including the Basel III correlation framework-with interactive models in Excel\/VBA. Wiley."},{"issue":"1","key":"4970_CR68","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s10479-016-2394-y","volume":"260","author":"L Mercuri","year":"2018","unstructured":"Mercuri, L., & Rroji, E. (2018). Risk parity for mixed tempered stable distributed sources of risk. Annals of Operations Research, 260(1), 375\u2013393.","journal-title":"Annals of Operations Research"},{"issue":"11","key":"4970_CR69","doi-asserted-by":"crossref","first-page":"1909","DOI":"10.1080\/14697688.2018.1439182","volume":"18","author":"M Michaelsen","year":"2018","unstructured":"Michaelsen, M., & Szimayer, A. (2018). Marginal consistent dependence modelling using weak subordination for Brownian motions. Quantitative Finance, 18(11), 1909\u20131925.","journal-title":"Quantitative Finance"},{"issue":"1","key":"4970_CR70","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1214\/aop\/1176995609","volume":"6","author":"I Monroe","year":"1978","unstructured":"Monroe, I. (1978). Processes that can be embedded in Brownian motion. The Annals of Probability, 6(1), 42\u201356.","journal-title":"The Annals of Probability"},{"issue":"3","key":"4970_CR71","doi-asserted-by":"crossref","first-page":"703","DOI":"10.2307\/1913610","volume":"55","author":"WK Newey","year":"1987","unstructured":"Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703\u2013708.","journal-title":"Econometrica"},{"key":"4970_CR72","unstructured":"Prause, K. (1999). The generalized hyperbolic model: Estimation, financial derivatives, and risk measures. PhD thesis, Albert-Ludwigs-Universit\u00e4t zu Freiburg im Breisgau."},{"issue":"1","key":"4970_CR73","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1023\/B:STCO.0000009419.12588.da","volume":"14","author":"RS Protassov","year":"2004","unstructured":"Protassov, R. S. (2004). EM-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with fixed $$\\lambda $$. Statistics and Computing, 14(1), 67\u201377.","journal-title":"Statistics and Computing"},{"key":"4970_CR74","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2019.121386","volume":"532","author":"AW Rathgeber","year":"2019","unstructured":"Rathgeber, A. W., Stadler, J., & St\u00f6ckl, S. (2019). Financial modelling applying multivariate L\u00e9vy processes: New insights into estimation and simulation. Physica A: Statistical Mechanics and its Applications, 532, 121386.","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"issue":"2","key":"4970_CR75","doi-asserted-by":"crossref","first-page":"17","DOI":"10.21314\/JOR.2000.023","volume":"2","author":"R Rebonato","year":"1999","unstructured":"Rebonato, R., & J\u00e4ckel, P. (1999). The most general methodology to create a valid correlation matrix for risk management and option pricing purposes. Journal of Risk, 2(2), 17\u201327.","journal-title":"Journal of Risk"},{"key":"4970_CR76","doi-asserted-by":"crossref","DOI":"10.1201\/9781315144597","volume-title":"Handbook of financial risk management","author":"T Roncalli","year":"2020","unstructured":"Roncalli, T. (2020). Handbook of financial risk management. Chapman and Hall\/CRC."},{"key":"4970_CR77","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/j.spa.2006.10.003","volume":"117","author":"J Rosinski","year":"2007","unstructured":"Rosinski, J. (2007). Tempering stable processes. Stochastic Processes and Their Applications, 117, 677\u2013707.","journal-title":"Stochastic Processes and Their Applications"},{"key":"4970_CR78","volume-title":"L\u00e9vy processes and infinitely divisible distributions","author":"K Sato","year":"1999","unstructured":"Sato, K. (1999). L\u00e9vy processes and infinitely divisible distributions. Cambridge University Press."},{"issue":"8","key":"4970_CR79","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S0219024908004701","volume":"11","author":"P Semeraro","year":"2008","unstructured":"Semeraro, P. (2008). A multivariate variance gamma model for financial application. International Journal of Theoretical and Applied Finance, 11(8), 1\u201318.","journal-title":"International Journal of Theoretical and Applied Finance"},{"key":"4970_CR80","doi-asserted-by":"crossref","first-page":"2339","DOI":"10.1080\/03610926.2019.1571609","volume":"49","author":"P Semeraro","year":"2020","unstructured":"Semeraro, P. (2020). A note on the multivariate generalized asymmetric Laplace motion. Communications in Statistics-Theory and Methods, 49, 2339\u20132355.","journal-title":"Communications in Statistics-Theory and Methods"},{"key":"4970_CR81","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/978-0-8176-8180-7_8","volume-title":"Handbook of computational and numerical methods in finance","author":"S Stoyanov","year":"2004","unstructured":"Stoyanov, S., & Racheva-Iotova, B. (2004). Numerical methods for stable modeling in financial risk management. In S. T. Rachev (Ed.), Handbook of computational and numerical methods in finance (pp. 299\u2013329). Birkh\u00e4user."},{"key":"4970_CR82","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/978-3-319-25826-3_7","volume-title":"The fascination of probability, statistics and their applications: In honour of Ole E. Barndorff-Nielsen","author":"P Tankov","year":"2016","unstructured":"Tankov, P. (2016). L\u00e9vy copulas: Review of recent results. In M. Podolskij, R. Stelzer, S. Thorbj\u00f8rnsen, & A. E. D. Veraart (Eds.), The fascination of probability, statistics and their applications: In honour of Ole E. Barndorff-Nielsen (pp. 127\u2013151). Springer International Publishing."},{"key":"4970_CR83","unstructured":"Tassinari, G. L. (2009). Pricing equity and debt tranches of collateralized funds of hedge fund obligations. PhD thesis, University of Bergamo."},{"issue":"4","key":"4970_CR84","doi-asserted-by":"crossref","first-page":"1450023","DOI":"10.1142\/S021902491450023X","volume":"17","author":"GL Tassinari","year":"2014","unstructured":"Tassinari, G. L., & Bianchi, M. L. (2014). Calibrating the smile with multivariate time-changed Brownian motion and the Esscher transform. International Journal of Theoretical and Applied Finance, 17(4), 1450023.","journal-title":"International Journal of Theoretical and Applied Finance"},{"issue":"12","key":"4970_CR85","doi-asserted-by":"crossref","first-page":"1991","DOI":"10.1080\/14697688.2012.749574","volume":"13","author":"GL Tassinari","year":"2013","unstructured":"Tassinari, G. L., & Corradi, C. (2013). Pricing equity and debt tranches of collateralized funds of hedge fund obligations: An approach based on stochastic time change and Esscher-transformed martingale measure. Quantitative Finance, 13(12), 1991\u20132010.","journal-title":"Quantitative Finance"},{"key":"4970_CR86","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/978-3-319-02499-8_25","volume-title":"Mathematical and statistical methods for actuarial sciences and finance","author":"GL Tassinari","year":"2014","unstructured":"Tassinari, G. L., & Corradi, C. (2014). Valuation of collateralized funds of hedge fund obligations: A basket option pricing approach. In M. Corazza & C. Pizzi (Eds.), Mathematical and statistical methods for actuarial sciences and finance (pp. 277\u2013288). Springer."},{"issue":"1","key":"4970_CR87","first-page":"95","volume":"44","author":"YC Wu","year":"2009","unstructured":"Wu, Y. C., Liao, S. L., & Shyu, S. D. (2009). Closed-form valuations of basket options using a multivariate normal inverse Gaussian model. Insurance: Mathematics and Economics, 44(1), 95\u2013102.","journal-title":"Insurance: Mathematics and Economics"},{"issue":"3","key":"4970_CR88","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1080\/00949655.2021.1962878","volume":"92","author":"Y Xia","year":"2022","unstructured":"Xia, Y., & Grabchak, M. (2022). Estimation and simulation for multivariate tempered stable distributions. Journal of Statistical Computation and Simulation, 92(3), 451\u2013475.","journal-title":"Journal of Statistical Computation and Simulation"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04970-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-022-04970-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-04970-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T10:02:41Z","timestamp":1758621761000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-022-04970-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,20]]},"references-count":88,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["4970"],"URL":"https:\/\/doi.org\/10.1007\/s10479-022-04970-3","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,20]]},"assertion":[{"value":"31 August 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}