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Optimal Investment for Insurers with the Extended CIR Interest Rate Model

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  • Mei Choi Chiu
  • Hoi Ying Wong

Abstract

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.

Suggested Citation

  • Mei Choi Chiu & Hoi Ying Wong, 2014. "Optimal Investment for Insurers with the Extended CIR Interest Rate Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:129474
    DOI: 10.1155/2014/129474
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    References listed on IDEAS

    as
    1. Cox, John C. & Ingersoll Junior, Jonathan E. & Ross, Stephen A., 2007. "A theory of the term structure of interest rates," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 47(2), April.
    2. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    3. Hoi Ying Wong & Mei Choi Chiu, 2013. "Homotopy Analysis Method for Boundary-Value Problem of Turbo Warrant Pricing under Stochastic Volatility," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, March.
    4. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2000. "Optimal investment strategies in a CIR framework," ULB Institutional Repository 2013/7594, ULB -- Universite Libre de Bruxelles.
    5. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    6. Chiu, Mei Choi & Wong, Hoi Ying, 2013. "Optimal investment for an insurer with cointegrated assets: CRRA utility," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 52-64.
    7. Hao Chang & Xi-min Rong, 2013. "An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Hao Chang & Xi-min Rong, 2013. "An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    9. Hoi Ying Wong & Mei Choi Chiu, 2013. "Homotopy Analysis Method for Boundary‐Value Problem of Turbo Warrant Pricing under Stochastic Volatility," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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