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

Kai Yin KWOK, Mei Choi CHIU, Hoi Ying WONG

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6 Citations (Scopus)

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. Copyright © 2016 Elsevier Ltd.
Original languageEnglish
Pages (from-to)353-366
JournalInsurance: Mathematics and Economics
Volume71
Early online dateOct 2016
DOIs
Publication statusPublished - Nov 2016

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Citation

Kwok, K. Y., Chiu, M. C., & Wong, H. Y. (2016). Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration. Insurance: Mathematics and Economics, 71, 353-366.

Keywords

  • Nonzero sum games
  • Longevity security market
  • Cointegration
  • Relative performance