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A fundamental challenge for insurance companies (insurers) is to strike the best balancebetween optimal investment and risk management of paying insurance liabilities, especiallyin a low interest rate environment. The stochastic interest rate becomes a criticalfactor in this asset-liability management (ALM) problem. This paper derives the closed-formsolution to the optimal investment problem for an insurer subject to the insurance liabilityof compound Poisson process and the stochastic interest rate following the extendedCIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochasticinterest rate when she invests in stocks and bonds. Our problem involves maximizing theexpected constant relative risk averse (CRRA) utility function subject to stochastic interestrate and Poisson shocks. After solving the stochastic optimal control problem with theHJB framework, we offer a verification theorem by proving the uniform integrability of atight upper bound for the objective function

Optimal Investment for Insurers with the Extended CIR Interest Rate Model