"A bias-corrected Least-Squares Monte Carlo and optimal decisions in retirement" by Pavel Shevchenko (Macquarie University, Australia)

Event Date: 

Monday, April 17, 2023 - 3:30pm to 4:30pm

Event Location: 

  • Sobel room (SH 5607F)

Research seminar by Pavel Shevchenko, Professor at the Department of Actuarial Studies and Business Analytics and Co-Director of the Centre for Risk Analytics at Macquarie Business School, Australia.

Title: A bias-corrected Least-Squares Monte Carlo and optimal decisions in retirement

Abstract: The Least-Squares Monte Carlo (LSMC) method has gained popularity in recent years due to its ability to handle multi-dimensional stochastic control problems, including problems with state variables affected by control. However, when applied to the stochastic control problems in the multi-period expected utility models, the regression fit tends to contain errors which accumulate over time and typically blow up the numerical solution. In this study we propose to transform the value function of the problems to improve the regression fit, and then using either the smearing estimate or smearing estimate with controlled heteroskedasticity to avoid the re-transformation bias in the estimates of the conditional expectations calculated in the LSMC algorithm. We also present and utilise recent improvements in the LSMC algorithms such as control randomisation with policy iteration to avoid accumulation of regression errors over time. Presented numerical examples demonstrate that transformation method leads to an accurate solution. In addition, in the forward simulation stage of the control randomisation algorithm, we propose a re-sampling of the state and control variables in their full domain at each time t and then simulating corresponding state variables at t+1, to improve the exploration of the state space that also appears to be critical to obtain a stable and accurate solution for the expected utility models. We present results of the method applied to finding optimal decisions for annuitisation, housing and reverse mortgage in retirement.
This talk is based on the following papers:
- Johan G. Andréasson and Pavel V. Shevchenko (2022). A bias-corrected Least-Squares Monte Carlo for solving multi-period utility models. European Actuarial Journal 12, pp. 349-379 available at https://ssrn.com/abstract=2985828. https://doi.org/10.1007/s13385-021-00288-9
- Johan G. Andréasson and Pavel V. Shevchenko (2021). Optimal annuitisation, housing and reverse mortgage in retirement in the presence of means-tested public pension. Available at SSRN: https://ssrn.com/abstract=2985830