Methods for Pricing American Options under Regime

We analyze a number of techniques for pricing American options under a regime 4 switching stochastic process. The techniques analyzed include both explicit and implicit discretiza5 tions with the focus being on methods which are unconditionally stable. In the case of implicit 6 methods we also compare a number of iterative procedures for solving the associated nonlinear al7 gebraic equations. Numerical tests indicate that a fixed point policy iteration, coupled with a direct 8 control formulation, is a reliable general purpose method. Finally we remark that we formulate the 9 American problem as an abstract optimal control problem, hence our results are applicable to more 10 general problems as well. 11