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Power Utility Maximization in an Exponential Lévy Model Without a Risk-free Asset

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Abstract

We consider the problem of maximizing the expected power utility from terminal wealth in a market where logarithmic securities prices follow a Lévy process. By Girsanov’s theorem, we give explicit solutions for power utility of undiscounted terminal wealth in terms of the Lévy-Khintchine triplet.

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References

  1. Benth, F., Karlsen, K., Reikvam, K. Optimal portfolio selection with consumption and nonlinear integrodifferential equations with gradient constraint: A viscosity solution approach. Finance Stochast, 5:257–303 (2001)

    Google Scholar 

  2. Emmer, S., Klüppelberg, C. Optimal portfolios when stock prices follow an exponential Lévy process. Finance & Stochastics, 8:17–44 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Framstad, N., Øksendal, B., Sulem, A. Optimal consumption and portfolio in a jump difussion market with proportional transaction costs. Journal of Mathematical Economics, 35:233–257 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fujiwara, T., Miyahara, Y. The minimal entropy martingale measures for geometric Lévy processes. Finance Stochast, 7:509–531 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Goll, T. and Kallsen, J., Optimal portfolios for logarithmic utility. stochastic process. Appl., 89:31–48 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. He, S., Wang, J., Yan, J. Semimartingale theory and stochastic calculus. Science Press, Beijing, CRC Press, Boca Raton, FL, 1992

  7. Jacod, J., Shiryaev, A. Limit theorems for stochastic processes. Springer-Verlag, Berlin, 1987

  8. Kallsen, J. Optimal portfolios for exponential Lévy processes. Math. Method Oper. Res., 51:357–374 (2000)

    Article  MathSciNet  Google Scholar 

  9. Korn, R., Optimal portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time. World Scientific, Singapore, 1997

  10. Merton, R. Lifetime portfolio selection under uncertainty: The continuous-time case. The Review of Economics and Statistics, 51:247–257 (1969)

    Article  Google Scholar 

  11. Merton, R. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3:373–413 (1971)

    Article  MathSciNet  Google Scholar 

  12. Xia, J., Yan, J.A. A new look at some basic concepts in arbitrage pricing theory. Science in China (Ser. A), 46:764–774 (2003)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

    Qing Zhou

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  1. Qing Zhou
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Correspondence to Qing Zhou.

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Zhou, Q. Power Utility Maximization in an Exponential Lévy Model Without a Risk-free Asset. Acta Mathematicae Applicatae Sinica, English Series 21, 145–152 (2005). https://doi.org/10.1007/s10255-005-0225-z

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  • DOI: https://doi.org/10.1007/s10255-005-0225-z

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