Numerical Methods in Financial and Actuarial Applications: A Stochastic Maximum Principle Approach

摘要

While numerical approaches to solve financial and actuarial stochastic optimization problems are usually based on dynamic programming, we explore an approach through a stochastic maximum principle formulation followed by the use of least squares regression to determine the optimal control policy. We show that this methodology can be applied to a number of realistic financial and actuarial problems of increasing complexity to highlight potential strengths and applications of this approach. We cast a direct connection between this approach and the stochastic duality approach to stochastic optimization. In particular, we discuss the potential improvements which can derive from this reformulation in terms of numerical precision and in order to provide bounds to control the simulation errors. The critical numerical issue is shown to be the numerical computation of conditional expectations which is performed applying the approach of Longstaff and Schwartz [ 1 ].