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Utility maximization for Lévy switching models

Author

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  • Lioudmila Vostrikova

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique)

  • Yuchao Dong

Abstract

This article is devoted to the maximisation of HARA utilities of Lévy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Leibler processes, the expressions of the optimal strategies in progressively enlarged filtration for the maximisation of HARA utilities as well as the values of the corresponding maximal expected utilities. The example of Brownian switching model is presented to give the financial interpretation of the results.

Suggested Citation

  • Lioudmila Vostrikova & Yuchao Dong, 2018. "Utility maximization for Lévy switching models," Working Papers hal-01844635, HAL.
    • Handle: RePEc:hal:wpaper:hal-01844635
    Note: View the original document on HAL open archive server: https://hal.science/hal-01844635
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    References listed on IDEAS

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    1. Marcos Escobar & Daniela Neykova & Rudi Zagst, 2015. "Portfolio Optimization In Affine Models With Markov Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-46.
    2. François, Pascal & Gauthier, Geneviève & Godin, Frédéric, 2014. "Optimal hedging when the underlying asset follows a regime-switching Markov process," European Journal of Operational Research, Elsevier, vol. 237(1), pages 312-322.
    3. Esche, Felix & Schweizer, Martin, 2005. "Minimal entropy preserves the Lévy property: how and why," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 299-327, February.
    4. Robert J. Elliott & Carlton-James U. Osakwe, 2006. "Option Pricing for Pure Jump Processes with Markov Switching Compensators," Finance and Stochastics, Springer, vol. 10(2), pages 250-275, April.
    5. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
    6. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    7. Tahir Choulli & Christophe Stricker, 2005. "Minimal Entropy–Hellinger Martingale Measure In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 465-490, July.
    8. Robert Elliott & Tak Kuen Siu & Leunglung Chan, 2007. "Pricing Volatility Swaps Under Heston's Stochastic Volatility Model with Regime Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 41-62.
    9. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
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    Cited by:

    1. Misha Beek & Michel Mandjes & Peter Spreij & Erik Winands, 2020. "Regime switching affine processes with applications to finance," Finance and Stochastics, Springer, vol. 24(2), pages 309-333, April.

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    More about this item

    Keywords

    Lévy switching models; utility maximisation; dual approach; f-divergence minimal martingale measure; optimal strategy;
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