Title: A Backward Simulation Method for Stochastic Optimal Control Problems,
Abstract: A number of optimal decision problems with uncertainty can be formulated into
a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC)
algorithm is a popular numerical method to approach solutions of such
stochastic control problems as analytical solutions are not tractable in
general. This paper generalizes the LSMC algorithm proposed in Shen and Weng
(2017) to solve a wide class of stochastic optimal control models. Our
algorithm has three pillars: a construction of auxiliary stochastic control
model, an artificial simulation of the post-action value of state process, and
a shape-preserving sieve estimation method which equip the algorithm with a
number of merits including bypassing forward simulation and control
randomization, evading extrapolating the value function, and alleviating
computational burden of the tuning parameter selection. The efficacy of the
algorithm is corroborated by an application to pricing equity-linked insurance
products.