Approximated Snell envelope and its applications

This paper proposes some mild conditions on underlying stochastic process of optimal stopping and some approximations are proposed for Snell envelope techniques. The aim is to simplify the computation of conditional expectations which are necessary in obtaining the sequential backward Snell auxiliary process. Then, by applying these approximations to return process of a financial asset, the behaviors of optimal stopping times at which the expectation of return process is optimized are studied. Here, it is assumed that the mean corrected return process is of GARCH type.