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Optimal Portfolio Selection in an Itô–Markov Additive Market

Author

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  • Zbigniew Palmowski

    (Department of Applied Mathematics, Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland)

  • Łukasz Stettner

    (Institute of Mathematics, Polish Academy of Sciences, 00-656 Warsaw, Poland
    Vistula University, 02-787 Warsaw, Poland)

  • Anna Sulima

    (Faculty of Management, Computer Science and Finance, Wrocław University of Economics, 53-345 Wrocław, Poland)

Abstract

We study a portfolio selection problem in a continuous-time Itô–Markov additive market with prices of financial assets described by Markov additive processes that combine Lévy processes and regime switching models. Thus, the model takes into account two sources of risk: the jump diffusion risk and the regime switching risk. For this reason, the market is incomplete. We complete the market by enlarging it with the use of a set of Markovian jump securities, Markovian power-jump securities and impulse regime switching securities. Moreover, we give conditions under which the market is asymptotic-arbitrage-free. We solve the portfolio selection problem in the Itô–Markov additive market for the power utility and the logarithmic utility.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:34-:d:216912
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    References listed on IDEAS

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    2. Sulima Anna, 2021. "The Absence of Arbitrage on the Complete Black-Scholes-Merton Regime-Switching Lévy Market," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(3), pages 72-84, September.

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