Search

In this paper, the insurance company invests its wealth in a capital market composed of a riskless asset and a risky asset. The aggregate claim process of the insurance company is modeled by the Gamma process so as to make it closer to the reality. In practice, the insurance company provides not only those policies with large lose coverings but also policies with small ones. The Gamma process can describe this characteristic better than the compound Poisson process. It is assumed that the insurance company can purchase proportional reinsurance or excess-of-loss reinsurance. Two kinds of optimization problems are considered: maximizing the expected utility of the terminal wealth and minimizing the probability of ruin. For the problem of maximizing the expected utility of the terminal wealth, the explicit optimal value functions and optimal strategies are obtained. For the problem of minimizing the ruin probability, a sufficient condition for the optimal value function and the optimal strategy is obtained. [ABSTRACT FROM AUTHOR]

This paper considers an optimal investment and reinsurance problem for an insurer under the mean-variance criterion. The stochastic volatility of the stock price is modeled by a Cox-Ingersoll-Ross (CIR) process. By applying a backward stochastic differential equation (BSDE) approach, we obtain a BSDE related to the underlying investment and reinsurance problem. Then solving the BSDE leads to closed-form expressions for both the efficient frontier and the efficient strategy. In the end, numerical examples are presented to analyze the economic behavior of the efficient frontier. [ABSTRACT FROM AUTHOR]

In this paper, we study the optimal investment and optimal reinsurance problem for an insurer under the criterion of mean-variance. The insurer's risk process is modeled by a compound Poisson process and the insurer can invest in a risk-free asset and a risky asset whose price follows a jump-diffusion process. In addition, the insurer can purchase new business (such as reinsurance). The controls (investment and reinsurance strategies) are constrained to take nonnegative values due to nonnegative new business and no-shorting constraint of the risky asset. We use the stochastic linear-quadratic (LQ) control theory to derive the optimal value and the optimal strategy. The corresponding Hamilton-Jacobi-Bellman (HJB) equation no longer has a classical solution. With the framework of viscosity solution, we give a new verification theorem, and then the efficient strategy (optimal investment strategy and optimal reinsurance strategy) and the efficient frontier are derived explicitly. [ABSTRACT FROM AUTHOR]

In this paper we study the optimal excess-of-loss reinsurance and dividend strategy for maximizing the expected total discounted dividends received by shareholders until ruin time. Transaction costs and taxes are required when dividends occur. The problem is formulated as a stochastic impulse control problem. By solving the corresponding quasi-variational inequality, we obtain analytical solutions for the optimal return function and the optimal strategy. [ABSTRACT FROM AUTHOR]

In this paper, we consider optimal proportional reinsurance from an insurer's point of view to maximize the adjustment coefficient. We obtain the explicit expressions for the optimal results in the diffusion approximation case as well as in the jump-diffusion case. Further, we derive a sharper bound on the ruin probability. When the claim sizes are exponentially distributed, we can prove that the Lundberg's inequality also holds for the ruin probability in the diffusion approximation case. Some numerical examples are presented to show that the ruin probability in the diffusion approximation case sometimes underestimates the ruin probability. [ABSTRACT FROM AUTHOR]

This paper studies the optimal reinsurance and investment strategy for an insurer with two dependent classes of insurance business, where the claim number processes are correlated through a common shock. It is assumed that the insurer also faces the decision making of investing in a financial market with one risk-free asset and one risky asset following the Heston stochastic volatility (SV) model. The insurer is not allowed to short sell the risky asset. Under the mean–variance criterion, we consider the insurer's problem of maximizing the expected terminal wealth and, at the same time, minimizing the variance of the terminal wealth. Using the results of stochastic linear–quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we derive closed-form expressions for the optimal strategies and the efficient frontiers in terms of solutions to the BSDEs. Our approach shows how BSDEs can be used to solve mean–variance problems in insurance applications. Finally, economic behavior of the efficient frontiers is analyzed by using some numerical examples. [ABSTRACT FROM AUTHOR]