Bias-Corrected Least-Squares Monte Carlo for Utility Based Optimal Stochastic Control Problems

30 Pages Posted: 20 Jun 2018 Last revised: 23 Dec 2018

See all articles by Johan Andreasson

Johan Andreasson

University of Technology Sydney (UTS); CSIRO Australia

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Multiple version iconThere are 2 versions of this paper

Date Written: December 16, 2018

Abstract

The Least-Squares Monte Carlo method has gained popularity recent years due to its ability to handle multi-dimensional stochastic control problems without restrictions on the state dynamics, including problems with state variables affected by control. However, when applied to stochastic control problems in the multiperiod expected utility models, the regression t tends to contain errors which accumulate over time and typically blow up the numerical solution. In this paper we propose to transform the value function of stochastic control problems to improve the regression t, and then using either the 'Smearing Estimate' or 'Controlled Heteroskedasticity' to avoid the re-transformation bias. We also present and utilise recent improvements in Least-Squares Monte Carlo algorithms such as control randomisation with policy iteration to avoid regression errors from accumulating. Presented numerical examples demonstrate that our transformation method allows for control of disturbance terms to be handled correctly and leads to an accurate solution. In addition, in the forward simulation stage of the algorithm, we propose a re-sampling of state variables at each time step instead of simulating continuous paths, to improve the exploration of the state space that also appears to be important to obtain a stable and accurate solution for expected utility models.

Keywords: Dynamic programming, Least-Squares Monte Carlo, control randomisation, stochastic control, lifecycle modelling

JEL Classification: D91, G11, C61

Suggested Citation

Andreasson, Johan and Shevchenko, Pavel V., Bias-Corrected Least-Squares Monte Carlo for Utility Based Optimal Stochastic Control Problems (December 16, 2018). Macquarie University Faculty of Business & Economics Research Paper . Available at SSRN: https://ssrn.com/abstract=3200164 or http://dx.doi.org/10.2139/ssrn.3200164

Johan Andreasson

University of Technology Sydney (UTS) ( email )

15 Broadway, Ultimo
PO Box 123
Sydney, NSW 2007
Australia

CSIRO Australia ( email )

41 Boggo Rd
Dutton Park, Queensland
Australia

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

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