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A policy iteration algorithm for the American put option and free boundary control problems. (English) Zbl 1450.35299

Summary: We develop a solution method for American put options that directly employs the policy iteration principle of dynamic programming. The method iteratively improves exercise policies, obtains monotonically increasing value functions and converges quadratically under reasonable assumptions. We present a numerical implementation that exhibits these features. The same principle is also applied to obtain a monotonically improving policy iteration scheme for general free boundary optimal control problems.

MSC:

35R35 Free boundary problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in general)
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