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

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  • Kwok, Kai Yin
  • Chiu, Mei Choi
  • Wong, Hoi Ying

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.

Suggested Citation

  • Kwok, Kai Yin & Chiu, Mei Choi & Wong, Hoi Ying, 2016. "Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 353-366.
  • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:353-366
    DOI: 10.1016/j.insmatheco.2016.10.005
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    References listed on IDEAS

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    Cited by:

    1. Ewald, Christian-Oliver & Zhang, Aihua, 2017. "On the effects of changing mortality patterns on investment, labour and consumption under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 105-115.

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