Sharing of Longevity Basis Risk in Pension Schemes With Income-Drawdown Guarantees

26 Pages Posted: 10 Mar 2020

See all articles by Ankush Agarwal

Ankush Agarwal

affiliation not provided to SSRN

Christian-Oliver Ewald

University of Glasgow; Høgskole i Innlandet

Yongjie Wang

University of Glasgow

Date Written: February 7, 2020

Abstract

This work studies a stochastic optimal control problem for a pension scheme which provides an income-drawdown policy to its members after their retirement. To manage the scheme efficiently, the manager and members agree to share the investment risk based on a pre-decided risk-sharing rule. The objective is to maximise both sides' utilities by controlling the manager's investment in risky assets and members' benefit withdrawals. We use stochastic affine class models to describe the force of mortality of the members' population and consider a longevity bond whose coupon payment is linked to a survival index. In our framework, we also investigate the longevity basis risk, which arises when the members' and the longevity bond's reference populations show different mortality behaviours. By applying the dynamic programming principle to solve the corresponding HJB equations, we derive optimal solutions for the single- and sub-population cases. Our numerical results show that by sharing the risk, both manager and members increase their utility. Moreover, even in the presence of longevity basis risk, we demonstrate that the longevity bond acts as an effective hedging instrument.

Keywords: Pension scheme, longevity basis risk, mortality-linked instrument, stochastic control, dynamic programming principle

JEL Classification: G10, G11, G12, G22

Suggested Citation

Agarwal, Ankush and Ewald, Christian-Oliver and Wang, Yongjie, Sharing of Longevity Basis Risk in Pension Schemes With Income-Drawdown Guarantees (February 7, 2020). Available at SSRN: https://ssrn.com/abstract=3539714 or http://dx.doi.org/10.2139/ssrn.3539714

Ankush Agarwal

affiliation not provided to SSRN

Christian-Oliver Ewald

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Høgskole i Innlandet ( email )

Lillehammer, 2624
Norway

Yongjie Wang (Contact Author)

University of Glasgow ( email )

Adam Smith Business School
Glasgow, Scotland G12 8LE
United Kingdom

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