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Stochastic target games with controlled loss

  • Bruno Bouchard
  • Ludovic Moreau
  • Marcel Nutz
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    We 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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    Paper provided by in its series Papers with number 1206.6325.

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    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
    Handle: RePEc:arx:papers:1206.6325
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    1. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    2. Bruno Bouchard & Marcel Nutz, 2011. "Weak Dynamic Programming for Generalized State Constraints," Papers 1105.0745,, revised Oct 2012.
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