A sequential game and envelopes of stochastic processes
Douglas P. Kennedy · Stochastics · 1983
A game is considered in which at times n=0,1,Players I and II choose non-negative random variables Un, Vn respectively, and I pays to II the amount (VnXn)/Un where X = {Xn, n≧0} is a given sequence of non-negative random variables. The random variables Un, Vn, Xn are adapted to a given filtration and are restricted so that for given β>0 and γ≧1. The solution of this gameleads to the investigation of a certain recursive stochastic equation and to an approximation scheme for the Snell envelope of the process X.