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Optimal Smooth Portfolio Selection for an Insider

  • Yaozhong Hu (a1) and Bernt Øksendal (a2)

Abstract

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.

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Copyright

Corresponding author

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

References

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[2] Bernardo, A. E. (2001). Contractual restrictions on insider trading: a welfare analysis. Computation and economic theory. Econom. Theory 18, 735.
[3] Biagini, F. and Øksendal, B. (2005). A general stochastic calculus approach to insider trading. Appl. Math. Optimization 52, 167181.
[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, 137164.
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[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, 103130.
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[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. 93104.
[9] Pikovsky, I. and Karatzas, I. (1996). Anticipative portfolio optimization. Adv. Appl. Prob. 28, 10951122.
[10] Postel-Vinay, F. and Zylberberg, A. (1997). Insiders et persistance: un réexamen dans un modèle de concurrence monopolistique. Ann. Économ. Statist. 1997, 161181.
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[12] Russo, F. and Vallois, P. (2000). Stochastic calculus with respect to continuous finite quadratic variation processes. Stoch. Stoch. Reports 70, 140.

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