Abstract
We introduce an efficient numerical scheme for continuous time Dynkin games under model uncertainty. We use the Skorokhod embedding in order to construct recombining tree approximations. This technique allows us to determine convergence rates and to construct numerically optimal stopping strategies. We apply our method to several examples of game options.
Highlights
We propose an efficient numerical scheme for the computations of values of Dynkin games under volatility uncertainty
We model uncertainty by assuming that the stochastic processes X, Y, Z are path
Our setup can be viewed as a Dynkin game variant of
Summary
We propose an efficient numerical scheme for the computations of values of Dynkin games under volatility uncertainty. In [1], the authors presented a recombining trinomial tree based approximations for what is known as a G–expectation in the sense of Peng ([26]) They did not provide a rigorous proof for the convergence of their scheme and did not obtain error estimates. 0 is the right endpoint of the volatility uncertainty interval, n is the number of time steps and T is the maturity date This machinery allows to go in the reverse direction, namely for a given distribution on the trinomial tree we can find a “close” distribution on the canonical space which lies in our set of model uncertainty. The idea of using the Skorokhod embedding technique in order to obtain an exact sequence along stopping times was employed in a recent work [5] where the authors approximated a one dimensional time–homogeneous diffusion by recombining trinomial trees (and obtained the same error of order O(n−1/4)). We argue rigorously the link between Dynkin games and pricing of game options in the current setup of model uncertainty
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