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Optimal portfolios for exponential Lévy processes

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  • Jan Kallsen

Abstract

We consider the problem of maximizing the expected utility from consumption or terminal wealth in a market where logarithmic securities prices follow a Lévy process. More specifically, we give explicit solutions for power, logarithmic and exponential utility in terms of the Lévy-Khintchine triplet. In the first two cases, a constant fraction of current wealth should be invested in each of the securities, as is well-known for related discrete-time models and for Brownian motion. The situation is different for exponential utility. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Jan Kallsen, 2000. "Optimal portfolios for exponential Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 357-374, August.
    • Handle: RePEc:spr:mathme:v:51:y:2000:i:3:p:357-374
    DOI: 10.1007/s001860000048
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