# A Backward Simulation Method for Stochastic Optimal Control Problems

## TL;DR

This paper introduces a generalized backward simulation algorithm for stochastic optimal control problems, improving computational efficiency and accuracy over traditional methods, demonstrated through an insurance product pricing application.

## Contribution

The paper extends the Least-Squares Monte Carlo algorithm to a broader class of stochastic control models with novel simulation and estimation techniques.

## Key findings

- The algorithm bypasses forward simulation and control randomization.
- It avoids extrapolating the value function.
- It reduces computational burden in parameter tuning.

## 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.