Optimal Control Strategy For An Insurance Company With Bankruptcy Value

In this paper, we consider the optimal asset allocation strategy for an insurance company with bankruptcy value. In this model, the company not only has income cash-flow, but also can choose between two investment possibilities. One choice is a riskless asset with fixed rate of return r0 , the other is a risky asset with mean rate of return r1 > r0(Borrowing and short selling is neither allowed). The company chooses the optimal asset allocation strategy to maximize the objective function J ( x , ) R0 E{ 0e ct dRt e cP}Ï€= +∫τπ+Ï„Ï€, where R0 is the initial reserve of the company, c denotes the discount rate,Ï„Ï€is the bankruptcy time relative to the strategyÏ€and P represents the bankruptcy value. In this paper we try to find out the explicit solution of the optimal value function V ( x ) sup J ( x, ), it is not a easy work due to the complexity of the HJB equation, therefore some numerical methods should be introduced for solving this problem. In this paper we will use Markov chain finite difference method to approximate the company's wealth process, by defining discrete value function v h( x ), we first prove that v h( x ) is a increasing and concave function and then give out the convergence result of v h( x ) as hâ†'0. Finally, an iteration algorithm is designed and sensitivity analysis for some important parameters is carried out.