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Pareto-optimal risk exchange in a continuous-time economy: Application to target benefit pension

Published online by Cambridge University Press:  15 September 2025

Cheng Tao Open the ORCID record for Cheng Tao [Opens in a new window] ,
Yang Shen  and
Tak Kuen Siu
Cheng Tao*
Affiliation:
Nankai-Taikang College of Insurance and Actuarial Science, Nankai University, Tianjin, PR China
Yang Shen
Affiliation:
School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, Sydney, Australia
Tak Kuen Siu
Affiliation:
Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, Australia
*
Corresponding author: Cheng Tao; Email: taocheng@nankai.edu.cn
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Abstract

This paper studies a long-standing problem of risk exchange and optimal resource allocation among multiple entities in a continuous-time pure risk-exchange economy. We establish a novel risk exchange mechanism that allows entities to share and transfer risks dynamically over time. To achieve Pareto optimality, we formulate the problem as a stochastic control problem and derive explicit solutions for the optimal investment, consumption, and risk exchange strategies using a martingale method. To highlight practical applications of the solution to the proposed problem, we apply our results to a target benefit pension plan, featuring the potential benefits of risk sharing within this pension system. Numerical examples show the sensitivity of investment portfolios, the adjustment item, and allocation ratios to specific parameters. It is observed that an increase in the aggregate endowment process results in a rise in the adjustment item. Furthermore, the allocation ratios exhibit a positive correlation with the weights of the agents.

Keywords

Pareto-optimal risk exchangecontinuous-time economyinvestment and consumptiontarget benefit pensionlongevity risk

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 55 , Special Issue 3: Risk Sharing , September 2025 , pp. 615 - 643
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The International Actuarial Association

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