We introduce a new approximation algorithm for nonlinear functional of future portfolio value. We call it as “Implicit method” in contrast with calling existing method as “Explicit method”. In this paper, we show both “Implicit” and “Explicit” algorithms converge to true value using Stochastic mesh which is an typical example of American Monte Carlo methods. And we show the efficiency of “Implicit method” through the theoretical convergence order and numerical simulation.

EB00000003446K

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