A Backward Simulation Method for Stochastic Optimal Control Problems

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 ge...

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Bibliographic Details
Published inarXiv.org
Main Authors Shen, Zhiyi, Weng, Chengguo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.01.2019
Subjects
Algorithms
Computer simulation
Mathematical models
Numerical methods
Optimal control
Simulation
Stochastic processes
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Summary: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.
ISSN:2331-8422