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$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point

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  • S. Cawston
  • L. Vostrikova
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    Abstract

    We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change-point model and we give the conditions for the existence of f-divergence minimal equivalent martingale measure. Using the connection between utility maximisation and $f$-divergence minimisation, we obtain a general formula for optimal strategy in change-point case for initially enlarged filtration and also for progressively enlarged filtration in the case of exponential utility. We illustrate our results considering the Black-Scholes model with change-point.

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    File URL: http://arxiv.org/pdf/1004.3525
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1004.3525.

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    Date of creation: Apr 2010
    Date of revision: Jun 2011
    Handle: RePEc:arx:papers:1004.3525

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    Web page: http://arxiv.org/

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