Abstract and Applied Analysis

Optimal Investment for Insurers with the Extended CIR Interest Rate Model

Mei Choi Chiu and Hoi Ying Wong

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A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 129474, 12 pages.

First available in Project Euclid: 2 October 2014

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Chiu, Mei Choi; Wong, Hoi Ying. Optimal Investment for Insurers with the Extended CIR Interest Rate Model. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 129474, 12 pages. doi:10.1155/2014/129474. https://projecteuclid.org/euclid.aaa/1412278812

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  • S. Thind, “Nordic insurers face up to low rates hedging challe-nge,” 2013, http://www.risk.net/insurance-risk/feature/22636- 88/nordic-insurers-face-up-to-lowrates-hedging-challenge.
  • J. C. Cox, J. E. Ingersoll, Jr., and S. A. Ross, “A theory of the term structure of interest rates,” Econometrica, vol. 53, no. 2, pp. 385–407, 1985.
  • H. Y. Wong and M. C. Chiu, “Homotopy analysis method for boundary-value problem of turbo warrant pricing under stochastic volatility,” Abstract and Applied Analysis, vol. 2013, Article ID 682524, 5 pages, 2013.
  • G. Deelstra, M. Grasselli, and P.-F. Koehl, “Optimal investment strategies in a CIR framework,” Journal of Applied Probability, vol. 37, no. 4, pp. 936–946, 2000.
  • G. Deelstra, M. Grasselli, and P.-F. Koehl, “Optimal investment strategies in the presence of a minimum guarantee,” Insurance: Mathematics & Economics, vol. 33, no. 1, pp. 189–207, 2003.
  • R. Ferland and F. Watier, “Mean-variance efficiency with extended CIR interest rates,” Applied Stochastic Models in Business and Industry, vol. 26, no. 1, pp. 71–84, 2010.
  • H. Chang and X.-M. Rong, “An investment and consumption problem with CIR interest rate and stochastic volatility,” Abstract and Applied Analysis, vol. 2013, Article ID 219397, 12 pages, 2013.
  • H. Yang and L. Zhang, “Optimal investment for insurer with jump-diffusion risk process,” Insurance: Mathematics & Economics, vol. 37, no. 3, pp. 615–634, 2005.
  • M. C. Chiu and H. Y. Wong, “Mean-variance asset-liability management: cointegrated assets and insurance liability,” European Journal of Operational Research, vol. 223, no. 3, pp. 785–793, 2012.
  • M. C. Chiu and H. Y. Wong, “Optimal investment for an insurer with cointegrated assets: CRRA utility,” Insurance: Mathematics & Economics, vol. 52, no. 1, pp. 52–64, 2013.
  • C. Hipp and M. Plum, “Optimal investment for insurers,” Insurance: Mathematics & Economics, vol. 27, no. 2, pp. 215–228, 2000.
  • W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, vol. 25, Springer, New York, NY, USA, 1993.
  • H. Abou-Kandil, G. Freiling, V. Ionescu, and G. Jank, Matrix Riccati Equations in Control and Systems Theory, Birkhäuser, Basel, Switzerland, 2003.
  • G. Freiling and G. Jank, “Generalized Riccati difference and differential equation,” Linear Algebra and Its Applications, vol. 241–243, pp. 291–303, 1996.
  • J. Gallier, “The Schur complement and symmetric positive semidefinite (and definite) matrices,” 2010, http://www.cis.upenn.edu/$\sim\,\!$jean/schur-comp.pdf.
  • G. Freiling, G. Jank, and A. Sarychev, “Lyapunov-type functions and invariant sets for Riccati matrix differential equations,” in Proceedings of ECC, B. van Dooren, Ed., Brussels, Belgium, 1997.
  • T. W. Wong, M. C. Chiu, and H. Y. Wong, “Time-consistent mean-variance hedging of longevity risk: effect of cointegration,” Insurance: Mathematics and Economics, vol. 56, pp. 56–67, 2014.
  • M. C. Chiu and H. Y. Wong, “Mean-variance portfolio selection with correlation risk,” Journal of Computational and Applied Mathematics, vol. 263, pp. 432–444, 2014. \endinput