{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:26:55Z","timestamp":1759847215393,"version":"3.37.3"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T00:00:00Z","timestamp":1621641600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T00:00:00Z","timestamp":1621641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501105"],"award-info":[{"award-number":["11501105"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010791","name":"University of International Business and Economics","doi-asserted-by":"publisher","award":["302\/871703"],"award-info":[{"award-number":["302\/871703"]}],"id":[{"id":"10.13039\/100010791","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007710","name":"University of Connecticut","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100007710","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s10479-021-04125-w","type":"journal-article","created":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T11:02:31Z","timestamp":1621681351000},"page":"139-163","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Optimal Bitcoin trading with inverse futures"],"prefix":"10.1007","volume":"304","author":[{"given":"Jun","family":"Deng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huifeng","family":"Pan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuyu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7390-7979","authenticated-orcid":false,"given":"Bin","family":"Zou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,5,22]]},"reference":[{"issue":"1","key":"4125_CR1","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1002\/fut.22050","volume":"40","author":"C Alexander","year":"2020","unstructured":"Alexander, C., Choi, J., Park, H., & Sohn, S. (2020). Bitmex bitcoin derivatives: Price discovery, informational efficiency, and hedging effectiveness. Journal of Futures Markets, 40(1), 23\u201343.","journal-title":"Journal of Futures Markets"},{"issue":"3","key":"4125_CR2","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10436-019-00348-x","volume":"15","author":"B Angoshtari","year":"2019","unstructured":"Angoshtari, B., & Leung, T. (2019). Optimal dynamic basis trading. Annals of Finance, 15(3), 307\u2013335.","journal-title":"Annals of Finance"},{"issue":"7","key":"4125_CR3","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1002\/fut.22004","volume":"39","author":"DG Baur","year":"2019","unstructured":"Baur, D. G., & Dimpfl, T. (2019). Price discovery in bitcoin spot or futures? Journal of Futures Markets, 39(7), 803\u2013817.","journal-title":"Journal of Futures Markets"},{"key":"4125_CR4","doi-asserted-by":"crossref","unstructured":"Bragin, A. (2015). Inverse futures in bitcoin economy. Available at SSRN https:\/\/ssrn.com\/abstract=2713755.","DOI":"10.2139\/ssrn.2713755"},{"issue":"1","key":"4125_CR5","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s007800000023","volume":"5","author":"P Carr","year":"2001","unstructured":"Carr, P., Jin, X., & Madan, D. B. (2001). Optimal investment in derivative securities. Finance and Stochastics, 5(1), 33\u201359.","journal-title":"Finance and Stochastics"},{"key":"4125_CR6","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.econlet.2018.07.031","volume":"172","author":"S Corbet","year":"2018","unstructured":"Corbet, S., Lucey, B., Peat, M., & Vigne, S. (2018). Bitcoin futures\u2014what use are they? Economics Letters, 172, 23\u201327.","journal-title":"Economics Letters"},{"issue":"1","key":"4125_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0022-0531(89)90067-7","volume":"49","author":"JC Cox","year":"1989","unstructured":"Cox, J. C., & Huang, C.-F. (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 49(1), 33\u201383.","journal-title":"Journal of Economic Theory"},{"issue":"4","key":"4125_CR8","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1002\/fut.20472","volume":"31","author":"M Dai","year":"2011","unstructured":"Dai, M., Zhong, Y., & Kwok, Y. K. (2011). Optimal arbitrage strategies on stock index futures under position limits. Journal of Futures Markets, 31(4), 394\u2013406.","journal-title":"Journal of Futures Markets"},{"issue":"58","key":"4125_CR9","doi-asserted-by":"publisher","first-page":"6320","DOI":"10.1080\/00036846.2020.1789549","volume":"52","author":"J Deng","year":"2020","unstructured":"Deng, J., Pan, H., Zhang, S., & Zou, B. (2020). Minimum-variance hedging of bitcoin inverse futures. Applied Economics, 52(58), 6320\u20136337.","journal-title":"Applied Economics"},{"issue":"1","key":"4125_CR10","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0165-1889(90)90003-Y","volume":"14","author":"D Duffie","year":"1990","unstructured":"Duffie, D., & Jackson, M. O. (1990). Optimal hedging and equilibrium in a dynamic futures market. Journal of Economic Dynamics and Control, 14(1), 21\u201333.","journal-title":"Journal of Economic Dynamics and Control"},{"issue":"1","key":"4125_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/aoap\/1177005978","volume":"1","author":"D Duffie","year":"1991","unstructured":"Duffie, D., & Richardson, H. R. (1991). Mean-variance hedging in continuous time. Annals of Applied Probability, 1(1), 1\u201315.","journal-title":"Annals of Applied Probability"},{"key":"4125_CR12","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.jbankfin.2015.08.033","volume":"61","author":"M Escobar","year":"2015","unstructured":"Escobar, M., Ferrando, S., & Rubtsov, A. (2015). Robust portfolio choice with derivative trading under stochastic volatility. Journal of Banking & Finance, 61, 142\u2013157.","journal-title":"Journal of Banking & Finance"},{"key":"4125_CR13","unstructured":"Fleming, W. H., & Soner, H. M. (2006). Controlled Markov Processes and Viscosity Solutions (Vol. 25). Springer."},{"key":"4125_CR14","doi-asserted-by":"crossref","unstructured":"Giudici, P., & Polinesi, G. (2019). Crypto price discovery through correlation networks. Annals of Operations Research, Special Issue: Recent Developments in Financial Modeling and Risk Management:1\u201315.","DOI":"10.1007\/s10479-019-03282-3"},{"key":"4125_CR15","unstructured":"Hale, G., Krishnamurthy, A., Kudlyak, M., & Shultz, P. (2018). How futures trading changed bitcoin prices. FRBSF Economic Letter, 12."},{"key":"4125_CR16","doi-asserted-by":"crossref","unstructured":"Hudson, R., & Urquhart, A. (2019). Technical trading and cryptocurrencies. Annals of Operations Research, Special Issue on Networks and Risk Management:1\u201330.","DOI":"10.1007\/s10479-019-03357-1"},{"key":"4125_CR17","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.econlet.2018.10.031","volume":"174","author":"B Kapar","year":"2019","unstructured":"Kapar, B., & Olmo, J. (2019). An analysis of price discovery between bitcoin futures and spot markets. Economics Letters, 174, 62\u201364.","journal-title":"Economics Letters"},{"key":"4125_CR18","doi-asserted-by":"crossref","unstructured":"Karatzas, I., & Shreve, S. E. (1998). Methods of mathematical finance (Vol. 39). Springer.","DOI":"10.1007\/b98840"},{"key":"4125_CR19","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1016\/j.frl.2018.11.006","volume":"30","author":"G K\u00f6chling","year":"2019","unstructured":"K\u00f6chling, G., M\u00fcller, J., & Posch, P. N. (2019). Does the introduction of futures improve the efficiency of bitcoin? Finance Research Letters, 30, 367\u2013370.","journal-title":"Finance Research Letters"},{"issue":"4","key":"4125_CR20","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/s10690-016-9215-9","volume":"23","author":"T Leung","year":"2016","unstructured":"Leung, T., Li, J., Li, X., & Wang, Z. (2016). Speculative futures trading under mean reversion. Asia-Pacific Financial Markets, 23(4), 281\u2013304.","journal-title":"Asia-Pacific Financial Markets"},{"issue":"3","key":"4125_CR21","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1016\/S0304-405X(03)00118-1","volume":"69","author":"J Liu","year":"2003","unstructured":"Liu, J., & Pan, J. (2003). Dynamic derivative strategies. Journal of Financial Economics, 69(3), 401\u2013430.","journal-title":"Journal of Financial Economics"},{"issue":"3","key":"4125_CR22","doi-asserted-by":"publisher","first-page":"247","DOI":"10.2307\/1926560","volume":"51","author":"RC Merton","year":"1969","unstructured":"Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics, 51(3), 247\u2013257.","journal-title":"Review of Economics and Statistics"},{"issue":"4","key":"4125_CR23","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1016\/0022-0531(71)90038-X","volume":"3","author":"RC Merton","year":"1971","unstructured":"Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3(4), 373\u2013413.","journal-title":"Journal of Economic Theory"},{"key":"4125_CR24","unstructured":"Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system. Available on https:\/\/git.dhimmel.com\/bitcoin-whitepaper\/."},{"key":"4125_CR25","unstructured":"Narayanan, A., Bonneau, J., Felten, E., Miller, A., & Goldfeder, S. (2016). Bitcoin and cryptocurrency technologies: A comprehensive introduction. Princeton University Press."},{"key":"4125_CR26","doi-asserted-by":"publisher","first-page":"101230","DOI":"10.1016\/j.frl.2019.07.003","volume":"33","author":"H Sebasti\u00e3o","year":"2019","unstructured":"Sebasti\u00e3o, H., & Godinho, P. (2019). Bitcoin futures: An effective tool for hedging cryptocurrencies. Finance Research Letters, 33, 101230.","journal-title":"Finance Research Letters"},{"issue":"3","key":"4125_CR27","doi-asserted-by":"publisher","first-page":"59","DOI":"10.3905\/joi.3.3.59","volume":"3","author":"FA Sortino","year":"1994","unstructured":"Sortino, F. A., & Price, L. N. (1994). Performance measurement in a downside risk framework. Journal of Investing, 3(3), 59\u201364.","journal-title":"Journal of Investing"},{"issue":"2","key":"4125_CR28","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1111\/j.1467-9965.2009.00366.x","volume":"19","author":"LR Sotomayor","year":"2009","unstructured":"Sotomayor, L. R., & Cadenillas, A. (2009). Explicit solutions of consumption-investment problems in financial markets with regime switching. Mathematical Finance, 19(2), 251\u2013279.","journal-title":"Mathematical Finance"},{"issue":"1","key":"4125_CR29","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10479-008-0398-y","volume":"164","author":"W Yan","year":"2008","unstructured":"Yan, W., & Li, S. (2008). A class of portfolio selection with a four-factor futures price model. Annals of Operations Research, 164(1), 139.","journal-title":"Annals of Operations Research"},{"key":"4125_CR30","doi-asserted-by":"crossref","unstructured":"Yermack, D. (2015). Is bitcoin a real currency? An economic appraisal. In Handbook of digital currency (pp. 31\u201343). Elsevier.","DOI":"10.1016\/B978-0-12-802117-0.00002-3"},{"key":"4125_CR31","unstructured":"Yong, J., & Zhou, X. Y. (1999). Stochastic controls: Hamiltonian systems and HJB equations (Vol. 43). Springer."},{"key":"4125_CR32","first-page":"57","volume":"58","author":"B Zou","year":"2014","unstructured":"Zou, B., & Cadenillas, A. (2014). Optimal investment and risk control policies for an insurer: Expected utility maximization. Insurance: Mathematics and Economics, 58, 57\u201367.","journal-title":"Insurance: Mathematics and Economics"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04125-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-021-04125-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04125-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T15:29:56Z","timestamp":1628263796000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-021-04125-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,22]]},"references-count":32,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["4125"],"URL":"https:\/\/doi.org\/10.1007\/s10479-021-04125-w","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"type":"print","value":"0254-5330"},{"type":"electronic","value":"1572-9338"}],"subject":[],"published":{"date-parts":[[2021,5,22]]},"assertion":[{"value":"15 May 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}