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Optimal Smooth Portfolio Selection for an Insider

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Yaozhong Hu  and
Bernt Øksendal
Yaozhong Hu*
Affiliation:
University of Kansas
Bernt Øksendal*
Affiliation:
University of Oslo and Norwegian School of Economics and Business Administration
*
∗Postal address: Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142, USA. Email address: hu@math.ku.edu
∗∗Postal address: Center of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, Box 1053 Blindern, Oslo, N-0316, Norway. Email address: oksendal@math.uio.no
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Abstract

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We study the optimal portfolio problem for an insider, in the case where the performance is measured in terms of the logarithm of the terminal wealth minus a term measuring the roughness and the growth of the portfolio. We give explicit solutions in some cases. Our method uses stochastic calculus of forward integrals.

Keywords

Insider tradingoptimal portfolioenlargement of filtrationlog utilityinformation flow

MSC classification

Secondary: 60H40: White noise theory 60H05: Stochastic integrals 60G15: Gaussian processes
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 742 - 752
Copyright
Copyright © Applied Probability Trust 2007 

References

[1] Amendinger, J., Imkeller, P. and Schweizer, M. (1998). Additional logarithmic utility of an insider. Stoch. Process. Appl. 75, 263–286.Google Scholar
[2] Bernardo, A. E. (2001). Contractual restrictions on insider trading: a welfare analysis. Computation and economic theory. Econom. Theory 18, 7–35.CrossRefGoogle Scholar
[3] Biagini, F. and Øksendal, B. (2005). A general stochastic calculus approach to insider trading. Appl. Math. Optimization 52, 167–181.Google Scholar
[4] Föllmer, H., Wu, C.-T. and Yor, M. (1999). Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading. Stoch. Process. Appl. 84, 137–164.Google Scholar
[5] Huddart, S., Hughes, J. S. and Levine, C. B. (2001). Public disclosure and dissimulation of insider trades. Econometrica 69, 665–681.Google Scholar
[6] Imkeller, P., Pontier, M. and Weisz, F. (2001). Free lunch and arbitrage possibilities in a financial market model with an insider. Stoch. Process. Appl. 92, 103–130.CrossRefGoogle Scholar
[7] Itô, K. (1978). Extension of stochastic integrals. In Proc. Internat. Symp. Stoch. Differential Equat., John Wiley, New York, pp. 95–109.Google Scholar
[8] Luo, S. and Zhang, Q. (2002). Dynamic insider trading. In Applied Probability (Hong Kong, 1999; AMS/IP Stud. Adv. Math. 26), American Mathematical Society, Providence, RI, pp. 93–104.Google Scholar
[9] Pikovsky, I. and Karatzas, I. (1996). Anticipative portfolio optimization. Adv. Appl. Prob. 28, 1095–1122.CrossRefGoogle Scholar
[10] Postel-Vinay, F. and Zylberberg, A. (1997). Insiders et persistance: un réexamen dans un modèle de concurrence monopolistique. Ann. Économ. Statist. 1997, 161–181.Google Scholar
[11] Russo, F. and Vallois, P. (1993). Forward, backward and symmetric stochastic integration. Prob. Theory Relat. Fields 97, 403–421.Google Scholar
[12] Russo, F. and Vallois, P. (2000). Stochastic calculus with respect to continuous finite quadratic variation processes. Stoch. Stoch. Reports 70, 1–40.CrossRefGoogle Scholar