Optimal investment for insurers with correlation risk: Risk aversion and investment horizon

Mei Choi CHIU, Hoi Ying WONG

Research output: Contribution to journalArticlespeer-review

Abstract

This article investigates the optimal investment for insurers with correlation risk, with the variance–covariance matrix among risky financial assets evolving as a stochastic positive definite matrix process. Using the Wishart diffusion matrix process, we formulate the insurer’s investment problem as the maximization of the expected constant relative risk-averse utility function subject to stochastic correlation, stochastic volatilities, and Poisson shocks. We obtain the explicit closed-form investment strategy and optimal expected utility through the Hamilton–Jacobi–Bellman framework. A verification theorem is derived to prove the uniform integrability of a tight upper bound for the objective function. The economic implication is that a long-term stable optimal investment policy requires the insurer to maintain a high risk-aversion level when the financial market contains stochastic volatility and/or stochastic correlation. Copyright © 2017 The authors.
Original languageEnglish
Pages (from-to)207-227
JournalIMA Journal of Management Mathematics
Volume29
Issue number2
Early online dateApr 2017
DOIs
Publication statusPublished - Apr 2018

Citation

Chiu, M. C., & Wong, H. Y. (2018). Optimal investment for insurers with correlation risk: Risk aversion and investment horizon. IMA Journal of Management Mathematics, 29(2), 207-227. doi: 10.1093/imaman/dpx001

Keywords

  • Wishart process
  • Utility theory
  • Verification theorem
  • Correlation risk

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