Risk Minimizing Strategies for Tracking a Stochastic Target

Abstract : We consider a stochastic control problem of beating a stochastic benchmark. The problem is considered in an incomplete market setting with external economic factors. The investor preferences are modelled in terms of HARA-type utility functions and trading takes place in a finite time horizon. The objective of the investor is to minimize his expected loss from the outperformance of the benchmark compared to the portfolio terminal wealth, and to specify the optimal investment strategy. We prove that for considered loss functions the corresponding Bellman equation possesses a unique solution. This solution guaranties the existence of a well defined investment strategy. We prove also under which conditions the verification theorem for the obtained solution of the Bellman equation holds.
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Communication dans un congrès
Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.188-196, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_19〉
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Andrzej Palczewski. Risk Minimizing Strategies for Tracking a Stochastic Target. Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.188-196, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_19〉. 〈hal-01347537〉

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