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Optimal Control Problem Associated with Jump Processes

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Abstract

An optimal portfolio/control problem is considered for a two-dimen\-sional model in finance. A pair consisting of the wealth process and cumulutative consumption process driven by a geometric Lévy process is controlled by adapted processes. The value function appears and turns out to be a viscosity solution to some integro-differential equation, by using the Bellman principle.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ehime University, Matsuyama Ehime 7908577, Japan

    Yasushi Ishikawa

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  1. Yasushi Ishikawa
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Correspondence to Yasushi Ishikawa.

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Ishikawa, Y. Optimal Control Problem Associated with Jump Processes. Appl Math Optim 50, 21–65 (2004). https://doi.org/10.1007/s00245-004-0795-9

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  • DOI: https://doi.org/10.1007/s00245-004-0795-9

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