Applications of weak convergence for hedging of game options

Details Applications of weak convergence for hedging of game options Applications of weak convergence for hedging of game options

2009-08-25

arxiv.org/abs/0908.3661v3

Annals of Applied Probability 2010, Vol. 20, No. 5, 1891-1906

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP675 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP675

In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes $\{S^{(n)}\}_{n=0}^{\infty}$ to a limit process $S$ we prove convergence Dynkin's games values corresponding to $\{S^{(n)}\}_{n=0}^{\infty}$ to the Dynkin's game value corresponding to $S$. We use these results to approximate game options prices with path dependent payoffs in continuous time models by a sequence of game options prices in discrete time models which can be calculated by dynamical programming algorithms. In comparison to previous papers we work under more general convergence of underlying processes, as well as weaker conditions on the payoffs.

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