Skip to main content
SpringerLink
Log in

Models for Insider Trading with Finite Utility

  • Chapter
Paris-Princeton Lectures on Mathematical Finance 2004

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1919))

In these lecture notes we review through simple examples recent results on models for insider trading based on the theory of enlargement of filtrations and on anticipating calculus. In particular, we concentrate on the case of strong type of insiders. That is, insiders that have additional information in the a.s. sense. We explain how to treat the utility maximization problem for insiders in order to obtain models where the utility is finite. In the anticipating framework, we introduce models where the signal of the insider can not be revealed to the small trader even though the insider has an effect on the price (large trader effect).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amendinger, J., Imkeller, P., Schweizer, M., 1998. Additional logarithmic utility of an insider. Stochastic Proc. Appl., 75, 263-286.

    Article  MATH  MathSciNet  Google Scholar 

  2. Amendinger, J., 2000. Martingale representations theorems for initially enlarged filtrations. Stochastic Proc. Appl., 89, 101-116.

    Article  MATH  MathSciNet  Google Scholar 

  3. Amendinger, J., Becherer D., Schweizer, M., 2003. A monetary value for initial information in portfolio optimization. Finance and Stochastics, 7, 29-46.

    Article  MATH  MathSciNet  Google Scholar 

  4. Ankirchner, S., Dereich S., Imkeller P., 2006. The Shannon information of filtrations and the additional logarithmic utility of insiders. Ann. Probab., 34, 743-778.

    Article  MATH  MathSciNet  Google Scholar 

  5. Baudoin, F., 2003. Modelling anticipations in financial markets. In Paris-Princeton Lectures on Mathematical Finance 2002. Lecture Notes in Mathematics 1814, SpringerVerlag. Berlin.

    Google Scholar 

  6. Baudoin, F., 2002. Conditioned Stochastic Differential Equations and Application to Finance, Stochastic Proc. Appl., 100, 109-145.

    Article  MATH  MathSciNet  Google Scholar 

  7. Baudoin, F. Nguyen-Noc, L., 2004. The financial value of a weak information on a financial market. Finance and Stochastics 8, 415-435.

    Article  MATH  MathSciNet  Google Scholar 

  8. Back, K., 1992. Insider Trading in Continuous Time. Review of Financial Studies 5, 387-409.

    Article  Google Scholar 

  9. Biagini, F. and Øksendal B., 2005. A general stochastic calculus approach to insider trading. Applied Mathematics and Optimization, 52, 167-181.

    Article  MATH  MathSciNet  Google Scholar 

  10. Corcuera J. M., Imkeller P., Kohatsu-Higa A., Nualart D., 2004. Additional utility of insiders with imperfect dynamical information. Finance and Stochastics, 8, 437-450, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  11. Corcuera J.M., Guerra J., Nualart D., Schoutens W., 2006. Optimal investment in a Lévy market. Applied Mathematics and Optimization, 53, 279-309.

    Article  MATH  MathSciNet  Google Scholar 

  12. Chaumont L., Yor M., 2004. Exercises in Probability, Cambridge University Press.

    Google Scholar 

  13. Elliot R.J., Geman H., Korkie B.M., 1997. Portfolio optimization and contingent claim pricing with differential information. Stochastics and Stochastics Reports 60, 185-203.

    MathSciNet  Google Scholar 

  14. Elliot R.J., Jeanblanc M., 1999. Incomplete markets with jumps and informed agents. Math. Meth. Oper. Res. 50, 475-492.

    Article  Google Scholar 

  15. Föllmer, H. Imkeller P., 1993. Anticipation cancelled by a Girsanov transformation : a paradox on Wiener space”, Ann. Inst. Henri Poincaré, 29-4, 569-586.

    Google Scholar 

  16. Framstad N.C., Oksendal B., Sulem A., 1998. Optimal consumption and portfolio in a jump diffusion model. In Shiryaev, A., Sulem, A. (eds.), Proceedings of the Workshop on Mathematical Finance, INRIA, Paris.

    Google Scholar 

  17. Goll T., Kallsen J. 2000. Optimal Portfolios for Logarithmic Utility. Stochastic Processes and their Applications 89 (1), 31-48.

    Article  MATH  MathSciNet  Google Scholar 

  18. Goll T., Kallsen J. 2003. A Complete Explicit Solution to the Log-Optimal Portfolio Problem. The Annals of Applied Probability 13, 774-799.

    Article  MATH  MathSciNet  Google Scholar 

  19. Grorud, A., 2000. Asymmetric information in a financial market with jumps. International Journal of Theoretical and Applied Finance, 3, 641-659.

    Article  MATH  MathSciNet  Google Scholar 

  20. Grorud, A., Pontier, M., 1998. Insider Trading in a continuous Time Market Model. International Journal of Theoretical and Applied Finance 1, 331-347.

    Article  MATH  Google Scholar 

  21. . Ikeda, N., Watanabe, S., 1989. Stochastic Differential Equations and Diffusion Processes. North-Holland-Kodansha.

    Google Scholar 

  22. Imkeller, P., 1996. Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin’s calculus. Probab. Th. Rel . Fields 106, 105-135.

    Article  MATH  MathSciNet  Google Scholar 

  23. Imkeller, P., 1997. Enlargement of the Wiener filtration by a manifold valued random element via Malliavin’s calculus. In Statistics and Control of Stochastic Processes. The Lipster Festschrift, Y.M. Kabanov, B.L. Rosovskii, A.N. Shiryaev (eds.), World Scientific, Singapore.

    Google Scholar 

  24. Imkeller, P., 2002. Random times at which insiders can have free lunches. Stochastics and Stochastics Reports, 74, 465-487.

    Article  MATH  MathSciNet  Google Scholar 

  25. Imkeller, P., Pontier, M., Weisz, F., 2001. Free lunch and arbitrage possibilities in a financial market with an insider. Stochastic Proc. Appl. 92, 103-130.

    Article  MATH  MathSciNet  Google Scholar 

  26. Jacod, J., 1985. Grossissement initial, hypothèse (H’), et théorème de Girsanov. In : Grossissements de filtrations: exemples et applications. T Jeulin, M. Yor (eds.) Lect. Notes in Maths. 1118. Springer-Verlag. Berlin.

    Google Scholar 

  27. Jacod J., Protter P. 1988. Time reversal of Lévy processes. Ann. Probab. 16, 620-641.

    Article  MATH  MathSciNet  Google Scholar 

  28. Jeulin, T., 1980. Semi-martingales et groissessement de filtration. Lect. Notes in Maths. 833. Springer-Verlag, Berlin

    Google Scholar 

  29. Karatzas, I., Pikovsky, I., 1996. Anticipative portfolio optimization. Adv. Appl. Prob. 28, 1095-1122.

    Article  MATH  MathSciNet  Google Scholar 

  30. . Kohatsu-Higa A., Yamazato M., 2007. Enlargement of filtrations with random times for processes with jumps. Preprint.

    Google Scholar 

  31. . Kohatsu-Higa A., Yamazato M., 2007. Insider modelling and logarithmic utility in markets with jumps, Preprint.

    Google Scholar 

  32. Kohatsu-Higa A., Sulem, A., 2006. Utility maximization in an insider influenced market. Mathematical Finance, 16, 153-179.

    Article  MATH  MathSciNet  Google Scholar 

  33. Kyle, A., 1985. Continuous Auctions and Insider Trading. Econometrica 53, 1315-1335.

    Article  MATH  Google Scholar 

  34. Kunita H., 2003: Mathematical finance for price processes with jumps. Proccedings of the Kusatsu Congress. World Scientific 2003.

    Google Scholar 

  35. Mansuy, R., Yor, M., 2005. Harnesses, Lévy processes and Monsieur Jourdain. Stochastic Process. Appl. 115, 329-338.

    Article  MATH  MathSciNet  Google Scholar 

  36. Meyer, P. A., 1996. Probability and Potentials. Blaisdell Publishing Company, Waltham, Mass.

    Google Scholar 

  37. Nualart, D. , 1995. The Malliavin Calculus and Related Topics. Springer-Verlag. Berlin.

    MATH  Google Scholar 

  38. . Nualart, D., 1995. Analysis on Wiener space and anticipating calculus. In Lectures on Probability Theory and Statistics. Ecole d’eté de Probabilités de Saint-Flour XXV. Lecture Notes in Mathematics 1690. Springer-Verlag.

    Google Scholar 

  39. . Øksendal B., Sulem, A., 2005. Partial observation in an anticipative environment. To appear in Proceedings of the Kolmogorov conference 2003.

    Google Scholar 

  40. Protter, P., 2005. Stochastic Integration and Differential Equations. Springer-Verlag. New York.

    Google Scholar 

  41. Russo F., Vallois P., 1993. Forward, backward and symmetric stochastic integration. Probab. Th. Rel. Fields, 97, 403-421.

    Article  MATH  MathSciNet  Google Scholar 

  42. Russo F., Vallois P., 2000. Stochastic calculus with respect to continuous finite quadratic variation processes. Stochastics and Stochastics Reports, 70, 1-40.

    MATH  MathSciNet  Google Scholar 

  43. Russo F., Vallois P., 1995. The generalized covariation process and Itô formula. Stochastic Process. Appl., 59, 81-104.

    Article  MATH  MathSciNet  Google Scholar 

  44. . Sato K. 1999: Lévy processes and infinite divisible distributions. Cambridge University Press.

    Google Scholar 

  45. . Séminaire de Calcul Stochastique 1982/83, Université Paris VI, 1985. Grossissements de fitrations: exemples et applications. T Jeulin, M. Yor (eds.). Lect. Notes in Maths. 1118. Springer-Velag. Berlin

    Google Scholar 

  46. . Williams, D. 1991. Probability with martingales. Cambridge University Press.

    Google Scholar 

  47. Yor, M. Grossissement de filtrations et absolue continuite de noyaux. In : Grossissements de filtrations: exemples et applications. T Jeulin, M. Yor (eds.) Lect. Notes in Maths. 1118. Springer-Verlag. Berlin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Engineering Sciences, Osaka University, Machikaneyama Cho 1–3, 560-8531, Osaka, Japan

    Arturo Kohatsu-Higa

Authors
  1. Arturo Kohatsu-Higa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kohatsu-Higa, A. (2007). Models for Insider Trading with Finite Utility. In: Paris-Princeton Lectures on Mathematical Finance 2004. Lecture Notes in Mathematics, vol 1919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73327-0_3

Download citation

Publish with us

Policies and ethics

Search

Navigation