Stochastic target games with controlled loss
AbstractWe study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian uncertainty.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1206.6325.
Date of creation: Jun 2012
Date of revision: Apr 2014
Publication status: Published in Annals of Applied Probability 2014, Vol. 24, No. 3, 899-934
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-08 (All new papers)
- NEP-GTH-2012-07-08 (Game Theory)
- NEP-MIC-2012-07-08 (Microeconomics)
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- Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, Springer, vol. 3(3), pages 251-273.
- Bruno Bouchard & Marcel Nutz, 2011. "Weak Dynamic Programming for Generalized State Constraints," Papers 1105.0745, arXiv.org, revised Oct 2012.
- Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
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