Robust stochastic control and equivalent martingale measures
AbstractWe study a class of robust, or worst case scenario, optimal control problems for jump diffusions. The scenario is represented by a probability measure equivalent to the initial probability law. We show that if there exists a control that annihilates the noise coefficients in the state equation and a scenario which is an equivalent martingale measure for a specific process which is related to the control-derivative of the state process, then this control and this probability measure are optimal. We apply the result to the problem of consumption and portfolio optimization under model uncertainty in a financial market, where the price process S(t) of the risky asset is modeled as a geometric Itô-Lévy process. In this case the optimal scenario is an equivalent local martingale measure of S(t). We solve this problem explicitly in the case of logarithmic utility functions.
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Bibliographic InfoPaper provided by HAL in its series Working Papers with number inria-00573117.
Date of creation: 03 Mar 2011
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Note: View the original document on HAL open archive server: http://hal.inria.fr/inria-00573117/en/
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robust control; model uncertainty; worst case scenario; portfolio optimization; Lévy Market;
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