The Role of Longevity-Indexed Bond in Risk Management of Aggregated Defined Benefit Pension Scheme

Xiaoyi Zhang, Yanan Li and Junyi Guo ()
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Xiaoyi Zhang: School of Economics and Management, Hebei University of Technology, Tianjin 300401, China
Yanan Li: School of Finance, Capital University of Economics and Business, Beijing 100070, China
Junyi Guo: School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Risks, 2024, vol. 12, issue 3, 1-17

Abstract: Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan’s optimal risk management problem focusing on minimizing the solvency risk over a finite time horizon and to investigate the investment strategies in a market, comprising a longevity-indexed bond and a risk-free asset, under stochastic nominal interest rates. Using the dynamic programming technique in the stochastic control problem, we obtain the closed-form optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, a comparative analysis implicates that longevity-indexed bonds significantly reduce solvency risk compared to zero-coupon bonds, offering a strategic advantage in pension fund management. Besides the closed-form solution and the comparative study, another novelty of this study is the extension of actuarial liability (AL) and normal cost (NC) definitions, and we introduce the risk neutral valuation of liabilities in DB pension scheme with the consideration of mortality rate.

Keywords: longevity-indexed bond; DB pension plan; solvency risk management; asset allocation; stochastic optimal control; HJB equation (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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