Optimal investment for an insurer with cointegrated assets: CRRA utility

Mei Choi CHIU, Hoi Ying WONG

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

This paper considers the optimal investment problem for an insurer that invests in cointegrated assets subject to the random payments of insurance claims. The insurer’s objective is to maximize the expected utility of the terminal wealth subject to the cointegration dynamics of risky assets and the risk of paying out random liabilities with a compound Poisson process. We solve the continuous-time investment problems for the class of the constant relative risk averse utility function using the framework of the HJB equation. An explicit solution is derived by recognizing an exponential affine form in the derivation process. We then investigate the risk-preference of insurers toward statistical arbitrage from pairs-trading using the analytical results. Although a financial market with cointegrated risky assets implies the existence of statistical arbitrage opportunities, insurers may not be interested in those opportunities due to the social responsibility of a high level of risk aversion. However, if insurers are forced to trade cointegrated assets, the derived optimal solution enhances the investment performance. Copyright © 2012 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)52-64
JournalInsurance: Mathematics and Economics
Volume52
Issue number1
Early online dateNov 2012
DOIs
Publication statusPublished - Jan 2013

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Optimal Investment
Arbitrage
HJB Equation
Risk Function
Compound Poisson Process
Risk Aversion
Cointegration
Relative Risk
Expected Utility
Financial Markets
Explicit Solution
Utility Function
Insurance
Continuous Time
Optimal Solution
Maximise
Imply
Optimal investment
Assets
Insurer

Citation

Chiu, M. C., & Wong, H. Y. (2013). Optimal investment for an insurer with cointegrated assets: CRRA utility. Insurance: Mathematics and Economics, 52(1), 52-64.

Keywords

  • Optimal investment
  • Cointegration
  • Pairs-trading
  • Utility theory