Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration

Kai Yin Kwok, Mei Choi Chiu and Hoi Ying Wong

Insurance: Mathematics and Economics, 2016, vol. 71, issue C, 353-366

Abstract: This paper investigates the impact of relative performance concerns on the longevity risk transfer market. When an insurer concerns about the relative performance in a two-insurer economy, she maximizes the expected utility of her terminal wealth benchmarked against her competitor’s. The problem formulation for a general utility, a general interest rate process and cointegrated mortality rates uses a nonzero sum stochastic differential game approach. Explicit solution of the Nash equilibrium is derived for constant relative risk adverse insurers under the Vasicek-type stochastic interest and mortality rates. Existence and uniqueness of the Nash equilibrium are established for the CIR-type models, which rule out negative interest and mortality rates. While previous studies based on the single-agent approaches have shown a high investment demand in longevity bonds, the launch of it was unsuccessful in reality. Ours supplements that the demand is much lower subject to the relative performance concerns.

Keywords: Nonzero sum games; Longevity security market; Cointegration; Relative performance; Nash equilibrium; Demand of longevity bonds (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:71:y:2016:i:c:p:353-366

DOI: 10.1016/j.insmatheco.2016.10.005

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