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A SIMPLE AND NEARLY OPTIMAL INVESTMENT STRATEGY TO MINIMIZE THE PROBABILITY OF LIFETIME RUIN

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Partial differential equations

Published online by Cambridge University Press:  16 February 2022

Xiaoqing Liang  and
Virginia R. Young
Xiaoqing Liang
Affiliation:
Department of Statistics, School of Sciences, Hebei University of Technology, Tianjin300401, P. R. China E-Mail: liangxiaoqing115@hotmail.com
Virginia R. Young*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109, USA
*
E-Mail: vryoung@umich.edu
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Abstract

We study the optimal investment strategy to minimize the probability of lifetime ruin under a general mortality hazard rate. We explore the error between the minimum probability of lifetime ruin and the achieved probability of lifetime ruin if one follows a simple investment strategy inspired by earlier work in this area. We also include numerical examples to illustrate the estimation. We show that the nearly optimal probability of lifetime ruin under the simplified investment strategy is quite close to the original minimum probability of lifetime ruin under reasonable parameter values.

Keywords

Probability of lifetime ruinoptimal investmentstochastic controlcomparison resultsC61D81G22

MSC classification

Secondary: 35B51: Comparison principles 65M15: Error bounds
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 2 , May 2022 , pp. 619 - 643
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The International Actuarial Association

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Footnotes

†

X. Liang thanks the National Natural Science Foundation of China (11701139, 11571189), the Research Foundation for Returned Scholars of Hebei Province (C20200102), and the Natural Science Foundation of Hebei Province (A2018202057, A2020202033) for financial support.

‡

V. R. Young thanks the Cecil J. and Ethel M. Nesbitt Professorship of Actuarial Mathematics for financial support.

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