Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T13:49:24.906Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Virginia R. Young*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109, USA
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Barbi, E., Lagona, F., Marsili, M., Vaupel, J. W. and Wachter, K. W. (2018) The plateau of human mortality: Demography of longevity pioneers. Science, 360(6396), 1459–1461.CrossRefGoogle ScholarPubMed
Bayraktar, E., Hu, X. and Young, V. R. (2011) Minimizing the probability of lifetime ruin under stochastic volatility. Insurance Mathematics and Economics, 49(2), 194–206.CrossRefGoogle Scholar
Bayraktar, E. and Young, V. R. (2007) Minimizing the probability of lifetime ruin under borrowing constraints. Insurance: Mathematics and Economics, 41(1), 196–221.Google Scholar
Bayraktar, E. and Young, V. R. (2011) Proving regularity of the minimal probability of ruin via a game of stopping and control. Finance and Stochastics, 15(4), 785–818.CrossRefGoogle Scholar
Bayraktar, E. and Zhang, Y. (2015a) Minimizing the probability of lifetime ruin under ambiguity aversion. SIAM Journal on Control and Optimization, 53(1), 58–90.CrossRefGoogle Scholar
Bayraktar, E. and Zhang, Y. (2015b) Stochastic Perron’s method for the probability of lifetime ruin problem under transaction costs. SIAM Journal on Control and Optimization, 53(1), 91–113.CrossRefGoogle Scholar
Krylov, N. V. (1980) Controlled Diffusion Processes, Vol. 14. Springer Science & Business Media.CrossRefGoogle Scholar
Liang, X. and Young, V. R. (2019) Minimizing the probability of lifetime ruin: Two riskless assets with transaction costs. ASTIN Bulletin, 49(3), 847–883.CrossRefGoogle Scholar
Milevsky, M. A. (2020) Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age? Insurance: Mathematics and Economics, 92, 147–161.Google ScholarPubMed
Milevsky, M. A. and Robinson, C. (2000) Self-annuitization and ruin in retirement. North American Actuarial Journal, 4(4), 112–129.CrossRefGoogle Scholar
Moore, K. S. and Young, V. R. (2006) Optimal and simple, nearly-optimal rules for minimizing the probability of financial ruin in retirement. North American Actuarial Journal, 10(4), 145–161.CrossRefGoogle Scholar
Young, V. R. (2004) Optimal investment strategy to minimize the probability of lifetime ruin. North American Actuarial Journal, 8(4), 105–126.CrossRefGoogle Scholar
Young, V. R. and Zhang, Y. (2016) Lifetime ruin under ambiguous hazard rate. Insurance: Mathematics and Economics, 70, 125–134.Google Scholar