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Risk-sensitive portfolio optimization problem for a large trader with inside information

  • Hiroaki Hata
Original Paper Area 4
  • 6 Downloads

Abstract

We consider a financial model that captures the characteristics of a large trader and an insider. This trader has some influence on the dynamics of prices. Moreover, the information of the insider is the final price plus a blurring noise that disappears as the final time approaches. In such a setting, we try to obtain the explicit solution of a risk-sensitive portfolio optimization problem with a finite time horizon.

Keywords

Risk-sensitive control Stochastic factor model Insider trading HJB equation 

Mathematics Subject Classification

93E20 91B28 49L20 90C40 60J70 60H30 

Notes

Acknowledgements

The author thanks the anonymous referee for variable comments and suggestions. The author also thanks Professor A. Kohatsu-Higa for his helpful comments. This work is supported by Grant-in-Aid for Young Scientists (B) No. 15K17584 from the Japan Society for the Promotion of Science.

References

  1. 1.
    Back, K.: Insider trading in continuous time. Rev. Financ. Stud. 5, 387–409 (1992)CrossRefGoogle Scholar
  2. 2.
    Bensoussan, A.: Stochastic Control of Partially Observable Systems. Cambridge University Press, Cambridge (1992)Google Scholar
  3. 3.
    Corcuera, J.M., Imkeller, P., Kohatsu-Higa, A., Nualart, D.: Additional utility of insiders with imperfect dynamical information. Financ. Stoch. 8, 437–450 (2004)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Danilova, A., Monoyios, M., Ng, A.: Optimal investment with inside information and parameter uncertainty. Math. Financ. Econ. 3, 13–38 (2010)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Hata, H.: Risk-sensitive asset management in a general diffusion factor model: risk-seeking case. Jpn. J. Ind. Appl. Math. 34(1), 59–98 (2017)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Hata, H., Iida, Y.: A risk-sensitive stochastic control approach to an optimal investment problem with partial information. Financ. Stoch. 10, 395–426 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Hata, H., Kohatsu-Higa, A.: Two examples of an insider with medium/long term effects on the underlying. In: Recent Advances in Financial Engineering (Proceedings of KIER-TMU International Workshop on Financial Engineering 2010), pp. 19–42 (2011)Google Scholar
  8. 8.
    Hata, H., Kohatsu-Higa, A.: A market model with medium/long-term effects due to an insider. Quant. Financ. 13(3), 421–437 (2013)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Hata, H., Sekine, J.: Solving long term optimal investment problems with Cox–Ingersoll–Ross interest rates. Adv. Math. Econ. 8, 231–255 (2006)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Hata, H., Sekine, J.: Explicit solution to a certain non-ELQG risk-sensitive stochastic control problem. Appl. Math. Optim. 62(3), 341–380 (2010)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Imkeller, P., Sheu, S.J.: Malliavin’s Calculus in Insiders Models: Additional Utility and Free Lunches. Math. Financ. 1, 153–169 (2003)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Karatzas, I., Pikovsky, I.: Anticipative portfolio optimization. Adv. Appl. Probab. 28, 1095–1122 (1996)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Kohatsu-Higa, A.: Models for insider trading with finite utility. Paris-Princeton Lectures on Mathematical Finance Series: Lecture Notes in Mathematics, Vol. 1919, pp. 103–172 (2007)Google Scholar
  14. 14.
    Kohatsu-Higa, A., Sulem, A.: Utility maximization in an insider influenced market. Math. Financ. 16, 153–179 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Kohatsu-Higa, A., Yamazato, M.: Insider models with finite utility in markets with jumps. Appl. Math. Optim. 64, 217–255 (2011)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Pham, H.: A large deviations approach to optimal long term investment. Financ. Stoch. 7(2), 169–195 (2003)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Protter, P.: Stochastic Integration and Differential Equations. Springer, Berlin (2004)MATHGoogle Scholar
  18. 18.
    Sekine, J.: A note on long-term optimal portfolios under drawdown constraints. Adv. Appl. Probab. 38(3), 673–692 (2006)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationShizuoka UniversityShizuokaJapan

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