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Some stability results of optimal investment in a simple Lévy market

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  • Niu, Liqun

Abstract

We investigate some investment problems of maximizing the expected utility of the terminal wealth in a simple Lévy market, where the stock price is driven by a Brownian motion plus a Poisson process. The optimal investment portfolios are given explicitly under the hypotheses that the utility functions belong to the HARA, exponential and logarithmic classes. We show that the solutions for the HARA utility are stable in the sense of weak convergence when the parameters vary in a suitable way.

Suggested Citation

  • Niu, Liqun, 2008. "Some stability results of optimal investment in a simple Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 445-452, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:445-452
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    References listed on IDEAS

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    1. Elyès Jouini & Clotilde Napp, 2004. "Convergence of utility functions and convergence of optimal strategies," Finance and Stochastics, Springer, vol. 8(1), pages 133-144, January.
    2. Nualart, David & Schoutens, Wim, 2000. "Chaotic and predictable representations for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 109-122, November.
    3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    4. José Manuel Corcuera & David Nualart & Wim Schoutens, 2005. "Completion of a Lévy market by power-jump assets," Finance and Stochastics, Springer, vol. 9(1), pages 109-127, January.
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
    8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    10. Grasselli, Martino, 2003. "A stability result for the HARA class with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 611-627, December.
    11. repec:dau:papers:123456789/355 is not listed on IDEAS
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    Cited by:

    1. Zbigniew Palmowski & {L}ukasz Stettner & Anna Sulima, 2018. "Optimal portfolio selection in an It\^o-Markov additive market," Papers 1806.03496, arXiv.org.
    2. Zbigniew Palmowski & Łukasz Stettner & Anna Sulima, 2019. "Optimal Portfolio Selection in an Itô–Markov Additive Market," Risks, MDPI, vol. 7(1), pages 1-32, March.

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