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Optimal Investment in a Levy Market

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Abstract

In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.

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Authors and Affiliations

  1. Facultat de Matematiques, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain

    Jose Manuel Corcuera & David Nualart

  2. CEMAPRE and ISEG, Rua do Quelhas 6, 1200-781 Lisboa, Portugal

    Joao Guerra

  3. Katholieke Universiteit Leuven, U.C.S., W. De Croylaan 54, B-3001 Leuven, Belgium

    Wim Schoutens

Authors
  1. Jose Manuel Corcuera
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  2. Joao Guerra
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  3. David Nualart
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  4. Wim Schoutens
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Corresponding authors

Correspondence to Jose Manuel Corcuera, Joao Guerra, David Nualart or Wim Schoutens.

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Corcuera, J., Guerra, J., Nualart, D. et al. Optimal Investment in a Levy Market. Appl Math Optim 53, 279–309 (2006). https://doi.org/10.1007/s00245-005-0846-x

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  • DOI: https://doi.org/10.1007/s00245-005-0846-x

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