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

S. Cawston; L. Vostrikova

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arXiv · 1004.3525

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

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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BibTeX RIS

S. Cawston, L. Vostrikova. 2010-04-20. $F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point. https://arxiv.org/abs/1004.3525

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