Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 1: Festschrift for Bernt Øksendal
143
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A BSDE arising in an exponential utility maximization problem in a pure jump market model

&
Pages 240-258 | Received 17 Aug 2015, Accepted 13 Mar 2016, Published online: 01 Apr 2016

References

  • S. Ankirchner, G. Dimitroff, G. Heyne, and C. Pigorsch, Futures cross-hedging with a stationary basis, J. Financial Quant. Anal. 47(6) (2012), pp. 1361–1395.
  • S. Ankirchner and P. Imkeller, Hedging with residual risk: A BSDE approach, in Seminar on Stochastic Analysis, Random Fields and Applications VI, Progress Probability Vol. 63, Birkhäuser/Springer Basel AG, Basel, 2011. pp. 311–325.
  • I. Bardhan, and X. Chao, On martingale measures when asset returns have unpredictable jumps, Stoch. Process. Appl. 63(1) (1996), pp. 35–54.
  • H. Bauer, Measure and Integration Theory, Walter de Gruyter, Germany, Berlin, 2001.
  • D. Becherer, Bounded solutions to backward SDEs with jumps for utility optimization and indifference hedging, Ann. Appl. Probab. 16(4) (2006), pp. 2027–2054.
  • P. Carr, and R. Lee, Variation and share-weighted variation swaps on time-changed Lévy processes, Finance Stoch. 17(4) (2013), pp. 685–716.
  • P. Carr, R. Lee, and L. Wu, Variance swaps on time-changed Lévy processes, Finance Stoch. 16(2) (2012), pp. 335–355.
  • R. Cont, Empirical properties of asset returns: Stylized facts and statistical issues, Quant. Finance 1 (2001), pp. 223–236.
  • R. Cont and P. Tankov, Financial Modelling with Jump Processes, CRC Press, Boca Raton, 2004.
  • D.M. Guillaume, M.M. Dacorogna, R.D. Davé, U.A. Müller, R.B. Olsen, and O.V. Pictet, From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchang markets, Finance Stoch. 1 (1997), pp. 95–129.
  • S.W. He, J.G. Wang and J.A. Yan, Semimartingale Theory and Stochastic Calculus, Taylor & Francis, Beijing, China, 1992.
  • Y. Hu, P. Imkeller, and M. Müller, Utility maximization in incomplete markets, Ann. Appl. Probab. 15(3) (2005), pp. 1691–1712.
  • J. Kallsen, and A.N. Shiryaev, The cumulant process and Esscher’s change of measure, Finance Stoch. 6(4) (2002), pp. 397–428.
  • C. Kardaras, No-free-lunch equivalences for exponential Lévy models under convex constraints on investment, Math. Finance 19(2) (2009), pp. 161–187.
  • N. Kazamaki, A sufficient condition for the uniform integrability of exponential martingales, Math. Rep. Toyama Univ. 2 (1979), pp. 1–11.
  • A.E. Kyprianou, Introductory Lectures on Fluctuations of Lévy Processes with Applications, Springer, Berlin, Germany, 2006.
  • L. Mattner, Complex differentiation under the integral, Nieuw Arch. Wiskd 5/2(2) (2001), pp. 32–35.
  • M.-A. Morlais, Utility maximization in a jump market model, Stoch.: Int. J. Prob. Stoch. Process. 81(1) (2009), pp. 1–27.
  • M.-A. Morlais, A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem, Stoch. Process. Appl. 120(10) (2010), pp. 1966–1995.
  • B. Øksendal, and A. Sulem, Applied stochastic control of jump diffusions. Universitext, 2nd ed., Springer, Berlin, 2007.
  • P. Protter and K. Shimbo, No arbitrage and general semimartingales, in Markov Processes and Related Topics: A Festschrift for Thomas, G. Kurtz, ed., Institute of Mathematical Statistics, Beachwood, Ohio, 2008, pp. 267–283.
  • A. Richter, Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models, Stoch. Process. Appl. 124(11) (2014), pp. 3578–3611.
  • L.C.G. Rogers, and D. Williams, Diffusions, Markov Processes, and Martingales, Vol. 1, Cambridge, Cambridge University Press, 2000. Reprint of the second edition

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.