{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T17:42:33Z","timestamp":1777570953723,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T00:00:00Z","timestamp":1669507200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T00:00:00Z","timestamp":1669507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PID2020-116694GB-I00"],"award-info":[{"award-number":["PID2020-116694GB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PID2020-116694GB-I00"],"award-info":[{"award-number":["PID2020-116694GB-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003176","name":"Ministerio de Educaci\u00f3n, Cultura y Deporte","doi-asserted-by":"publisher","award":["FPU18\/01101"],"award-info":[{"award-number":["FPU18\/01101"]}],"id":[{"id":"10.13039\/501100003176","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The anticipative information refers to some information about future events that may be disclosed in advance. This information may regard, for example, financial assets and their future trends. In our paper, we assume the existence of some anticipative information in a market whose risky asset dynamics evolve according to a Brownian motion and a Poisson process. Using Malliavin calculus and filtration enlargement techniques, we derive the information drift of the mentioned processes and, both in the pure jump case and in the mixed one, we compute the additional expected logarithmic utility. Many examples are shown, where the anticipative information is related to some conditions that the constituent processes or their running maximum may verify, in particular, we show new examples considering Bernoulli random variables.<\/jats:p>","DOI":"10.1007\/s10479-022-05060-0","type":"journal-article","created":{"date-parts":[[2022,11,27]],"date-time":"2022-11-27T11:28:29Z","timestamp":1669548509000},"page":"1289-1314","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Anticipative information in a Brownian\u2212Poisson market"],"prefix":"10.1007","volume":"336","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1272-8352","authenticated-orcid":false,"given":"Bernardo","family":"D\u2019Auria","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9461-6038","authenticated-orcid":false,"given":"Jose A.","family":"Salmeron","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,11,27]]},"reference":[{"issue":"1","key":"5060_CR1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s007800200075","volume":"7","author":"J Amendinger","year":"2003","unstructured":"Amendinger, J., Becherer, D., & Schweizer, M. (2003). A monetary value for initial information in portfolio optimization. Finance and Stochastics, 7(1), 29\u201346. https:\/\/doi.org\/10.1007\/s007800200075","journal-title":"Finance and Stochastics"},{"issue":"2","key":"5060_CR2","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/S0304-4149(98)00014-3","volume":"75","author":"J Amendinger","year":"1998","unstructured":"Amendinger, J., Imkeller, P., & Schweizer, M. (1998). Additional logarithmic utility of an insider. Stochastic Processes and their Applications, 75(2), 263\u2013286. https:\/\/doi.org\/10.1016\/S0304-4149(98)00014-3","journal-title":"Stochastic Processes and their Applications"},{"issue":"9","key":"5060_CR3","doi-asserted-by":"publisher","first-page":"1662","DOI":"10.1016\/j.spa.2007.10.007","volume":"118","author":"S Ankirchner","year":"2008","unstructured":"Ankirchner, S. (2008). On filtration enlargements and purely discontinuous martingales. Stochastic Processes and their Applications, 118(9), 1662\u20131678. https:\/\/doi.org\/10.1016\/j.spa.2007.10.007","journal-title":"Stochastic Processes and their Applications"},{"key":"5060_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-020-03692-8","author":"M Bellalah","year":"2020","unstructured":"Bellalah, M., Hakim, A., Si, K., et al. (2020). Long term optimal investment with regime switching: Inflation, information and short sales. Annals of Operations Research. https:\/\/doi.org\/10.1007\/s10479-020-03692-8","journal-title":"Annals of Operations Research"},{"issue":"3","key":"5060_CR5","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1111\/1467-9965.02007","volume":"12","author":"HP Bermin","year":"2002","unstructured":"Bermin, H. P. (2002). A general approach to hedging options: Applications to barrier and partial barrier options. Mathematical Finance, 12(3), 199\u2013218. https:\/\/doi.org\/10.1111\/1467-9965.02007","journal-title":"Mathematical Finance"},{"issue":"4","key":"5060_CR6","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1007\/s11579-018-0217-4","volume":"12","author":"HN Chau","year":"2018","unstructured":"Chau, H. N., Runggaldier, W., & Tankov, P. (2018). Arbitrage and utility maximization in market models with an insider. Mathematics and Financial Economics, 12(4), 589\u2013614. https:\/\/doi.org\/10.1007\/s11579-018-0217-4","journal-title":"Mathematics and Financial Economics"},{"key":"5060_CR7","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/s10479-020-03596-7","volume":"299","author":"K Colaneri","year":"2021","unstructured":"Colaneri, K., Herzel, S., & Nicolosi, M. (2021). The value of knowing the market price of risk. Annals of Operations Research, 299, 101\u2013131. https:\/\/doi.org\/10.1007\/s10479-020-03596-7","journal-title":"Annals of Operations Research"},{"key":"5060_CR8","doi-asserted-by":"publisher","first-page":"437","DOI":"10.2139\/ssrn.428203","volume":"8","author":"J Corcuera","year":"2004","unstructured":"Corcuera, J., Imkeller, P., & Kohatsu-Higa, A. (2004). Additional utility of insiders with imperfect dynamical information. Finance and Stochastics, 8, 437\u2013450. https:\/\/doi.org\/10.2139\/ssrn.428203","journal-title":"Finance and Stochastics"},{"issue":"2","key":"5060_CR9","doi-asserted-by":"publisher","first-page":"998","DOI":"10.3934\/mbe.2020053","volume":"17","author":"B D\u2019Auria","year":"2020","unstructured":"D\u2019Auria, B., & Salmer\u00f3n, J. A. (2020). Insider information and its relation with the arbitrage condition and the utility maximization problem. Mathematical Biosciences and Engineering, 17(2), 998\u20131019. https:\/\/doi.org\/10.3934\/mbe.2020053","journal-title":"Mathematical Biosciences and Engineering"},{"key":"5060_CR10","doi-asserted-by":"publisher","unstructured":"Di Nunno, G., \u00d8ksendal, B., & Proske, F. (2009). Malliavin Calculus for L\u00e9vy Processes with Applications to Finance, 1st edn. Universitext, Springer, Berlin, Heidelberg, https:\/\/doi.org\/10.1007\/978-3-540-78572-9.","DOI":"10.1007\/978-3-540-78572-9"},{"issue":"03","key":"5060_CR11","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1142\/S0219025707002828","volume":"10","author":"G Di Nunno","year":"2007","unstructured":"Di Nunno, G. (2007). Random fields: non-anticipating derivative and differentiation formulas. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 10(03), 465\u2013481. https:\/\/doi.org\/10.1142\/S0219025707002828","journal-title":"Infinite Dimensional Analysis, Quantum Probability and Related Topics"},{"issue":"1","key":"5060_CR12","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1080\/14697680500467905","volume":"6","author":"G Di Nunno","year":"2006","unstructured":"Di Nunno, G., Meyer-Brandis, T., \u00d8ksendal, B., et al. (2006). Optimal portfolio for an insider in a market driven by L\u00e9vy processes. Quantitative Finance, 6(1), 83\u201394. https:\/\/doi.org\/10.1080\/14697680500467905","journal-title":"Quantitative Finance"},{"key":"5060_CR13","doi-asserted-by":"publisher","unstructured":"Diestel, J., & Uhl, J.J. (1977). Vector measures. American Mathematical Society, Providence, R.I., https:\/\/doi.org\/10.1090\/surv\/015, with a foreword by B. J. Pettis, Mathematical Surveys, No. 15.","DOI":"10.1090\/surv\/015"},{"issue":"4","key":"5060_CR14","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1287\/moor.2019.1028","volume":"45","author":"PA Ernst","year":"2020","unstructured":"Ernst, P. A., & Rogers, L. C. G. (2020). The value of insight. Mathematics of Operations Research, 45(4), 1193\u20131209. https:\/\/doi.org\/10.1287\/moor.2019.1028","journal-title":"Mathematics of Operations Research"},{"issue":"04","key":"5060_CR15","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1142\/S0219024900000802","volume":"03","author":"A Grorud","year":"2000","unstructured":"Grorud, A. (2000). Asymmetric information in a financial market with jumps. International Journal of Theoretical and Applied Finance, 03(04), 641\u2013659. https:\/\/doi.org\/10.1142\/S0219024900000802","journal-title":"International Journal of Theoretical and Applied Finance"},{"issue":"03","key":"5060_CR16","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1142\/S0219024998000199","volume":"01","author":"A Grorud","year":"1998","unstructured":"Grorud, A., & Pontier, M. (1998). Insider trading in a continuous time market model. International Journal of Theoretical and Applied Finance, 01(03), 331\u2013347. https:\/\/doi.org\/10.1142\/S0219024998000199","journal-title":"International Journal of Theoretical and Applied Finance"},{"issue":"1","key":"5060_CR17","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0304-4149(00)00071-5","volume":"92","author":"P Imkeller","year":"2001","unstructured":"Imkeller, P., Pontier, M., & Weisz, F. (2001). Free lunch and arbitrage possibilities in a financial market model with an insider. Stochastic Processes and their Applications, 92(1), 103\u2013130. https:\/\/doi.org\/10.1016\/S0304-4149(00)00071-5","journal-title":"Stochastic Processes and their Applications"},{"key":"5060_CR18","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BFb0075768","volume-title":"Grossissements de filtrations: exemples et applications","author":"J Jacod","year":"1985","unstructured":"Jacod, J. (1985). Grossissement initial, hypoth\u00e9se (H\u2019) et th\u00e9or\u00e9me de Girsanov. In T. Jeulin & M. Yor (Eds.), Grossissements de filtrations: exemples et applications (pp. 15\u201335). Berlin, Heidelberg: Springer. https:\/\/doi.org\/10.1007\/BFb0075768"},{"key":"5060_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-737-4","volume-title":"Mathematical methods for financial markets","author":"M Jeanblanc","year":"2009","unstructured":"Jeanblanc, M., Yor, M., & Chesney, M. (2009). Mathematical methods for financial markets (1st ed.). London: Springer. https:\/\/doi.org\/10.1007\/978-1-84628-737-4","edition":"1"},{"issue":"3","key":"5060_CR20","doi-asserted-by":"publisher","first-page":"429","DOI":"10.24033\/asens.1352","volume":"11","author":"T Jeulin","year":"1978","unstructured":"Jeulin, T., & Yor, M. (1978). Nouveaux r\u00e9sultats sur le grossissement des tribus. Annales scientifiques de l\u2019\u00c9cole normale sup\u00e9rieure, 11(3), 429\u2013443. https:\/\/doi.org\/10.24033\/asens.1352","journal-title":"Annales scientifiques de l\u2019\u00c9cole normale sup\u00e9rieure"},{"issue":"3","key":"5060_CR21","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1080\/15598608.2011.10412040","volume":"5","author":"Y Kakihara","year":"2011","unstructured":"Kakihara, Y. (2011). Radon\u2013Nikod\u00fdm derivatives of Hilbert space valued measures. Journal of Statistical Theory and Practice, 5(3), 453\u2013473. https:\/\/doi.org\/10.1080\/15598608.2011.10412040","journal-title":"Journal of Statistical Theory and Practice"},{"issue":"5","key":"5060_CR22","doi-asserted-by":"publisher","first-page":"1801","DOI":"10.1214\/09-AAP673","volume":"20","author":"A Kuznetsov","year":"2010","unstructured":"Kuznetsov, A. (2010). Wiener\u2013Hopf factorization and distribution of extrema for a family of L\u00e9vy processes. The Annals of Applied Probability, 20(5), 1801\u20131830. https:\/\/doi.org\/10.1214\/09-AAP673","journal-title":"The Annals of Applied Probability"},{"key":"5060_CR23","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s007800100055","volume":"6","author":"JA Le\u00f3n","year":"2002","unstructured":"Le\u00f3n, J. A., Sol\u00e9, J. L., Utzet, F., et al. (2002). On L\u00e9vy processes, Malliavin calculus and market models with jumps. Finance and Stochastics, 6, 197\u2013225. https:\/\/doi.org\/10.1007\/s007800100055","journal-title":"Finance and Stochastics"},{"key":"5060_CR24","doi-asserted-by":"publisher","unstructured":"Mandrekar, V., & R\u00fcdiger, B. (2015). Stochastic integration in Banach spaces. In: Probability theory and stochastic modelling (1st edn). Springer. https:\/\/doi.org\/10.1007\/978-3-319-12853-5","DOI":"10.1007\/978-3-319-12853-5"},{"issue":"1","key":"5060_CR25","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1081\/SAP-120017538","volume":"21","author":"M Mensi","year":"2003","unstructured":"Mensi, M., & Privault, N. (2003). Conditional calculus on Poisson space and enlargement of filtration. Stochastic Analysis and Applications, 21(1), 183\u2013204. https:\/\/doi.org\/10.1081\/SAP-120017538","journal-title":"Stochastic Analysis and Applications"},{"key":"5060_CR26","volume-title":"The Malliavin calculus and related topics. Probability and its applications","author":"D Nualart","year":"2006","unstructured":"Nualart, D. (2006). The Malliavin calculus and related topics. Probability and its applications. Berlin: Springer."},{"key":"5060_CR27","first-page":"154","volume":"24","author":"D Nualart","year":"1990","unstructured":"Nualart, D., & Vives, J. (1990). Anticipative calculus for the Poisson process based on the Fock space. S\u00e9minaire de probabilit\u00e9s de Strasbourg, 24, 154\u2013165.","journal-title":"S\u00e9minaire de probabilit\u00e9s de Strasbourg"},{"issue":"3\u20134","key":"5060_CR28","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1080\/17442509108833682","volume":"34","author":"DL Ocone","year":"1991","unstructured":"Ocone, D. L., & Karatzas, I. (1991). A generalized Clark representation formula, with application to optimal portfolios. Stochastics and Stochastic Reports, 34(3\u20134), 187\u2013220. https:\/\/doi.org\/10.1080\/17442509108833682","journal-title":"Stochastics and Stochastic Reports"},{"key":"5060_CR29","doi-asserted-by":"crossref","unstructured":"Protter, P. E. (2005). Stochastic integration and differential equations. Berlin, Heidelberg: Springer. https:\/\/doi.org\/10.1007\/978-3-662-10061-5.","DOI":"10.1007\/978-3-662-10061-5"},{"issue":"2","key":"5060_CR30","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.spa.2006.06.006","volume":"117","author":"J Sol\u00e9","year":"2007","unstructured":"Sol\u00e9, J., Utzet, F., & Vives, J. (2007). Canonical L\u00e9vy process and Malliavin calculus. Stochastic Processes and their Applications, 117(2), 165\u2013187. https:\/\/doi.org\/10.1016\/j.spa.2006.06.006","journal-title":"Stochastic Processes and their Applications"},{"issue":"5","key":"5060_CR31","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1080\/17442508.2017.1415340","volume":"90","author":"JA Wright","year":"2018","unstructured":"Wright, J. A., Yam, S. C. P., & Zhang, Z. (2018). Enlargement of filtration on Poisson space: A Malliavin calculus approach. Stochastics, 90(5), 682\u2013700. https:\/\/doi.org\/10.1080\/17442508.2017.1415340","journal-title":"Stochastics"}],"updated-by":[{"DOI":"10.1007\/s10479-022-05125-0","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T00:00:00Z","timestamp":1670976000000}}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-05060-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-022-05060-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-022-05060-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T19:07:32Z","timestamp":1715627252000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-022-05060-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,27]]},"references-count":31,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["5060"],"URL":"https:\/\/doi.org\/10.1007\/s10479-022-05060-0","relation":{"correction":[{"id-type":"doi","id":"10.1007\/s10479-022-05125-0","asserted-by":"object"}]},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,27]]},"assertion":[{"value":"1 November 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 December 2022","order":3,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":4,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":5,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1007\/s10479-022-05125-0","URL":"https:\/\/doi.org\/10.1007\/s10479-022-05125-0","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflicts of interest in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}