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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5 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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Stochastic Differential Games
Cointegration
Mortality Rate
Interest Rates
Nash Equilibrium
Stochastic Interest Rates
Relative Risk
Expected Utility
Explicit Solution
Existence and Uniqueness
Maximise
Formulation
Demand
Stochastic differential games
Insurer
Mortality rate
Relative performance
Nash equilibrium
Interest rates
Model

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