Optimal investment and proportional reinsurance with constrained control variables

2010 ◽  
Vol 32 (5) ◽  
pp. 587-608 ◽  
Author(s):  
Zhibin Liang ◽  
Lihua Bai ◽  
Junyi Guo
Keyword(s):  
Optimal Investment ◽  
Proportional Reinsurance ◽  
Constrained Control ◽  
Control Variables

scholarly journals RUIN PROBABILITIES UNDER AN OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE POLICY IN A JUMP DIFFUSION RISK PROCESS

2009 ◽  
Vol 51 (1) ◽  
pp. 34-48 ◽  
Author(s):  
YIPING QIAN ◽  
XIANG LIN
Keyword(s):  
Ruin Probability ◽  
Market Price ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Risk Process ◽  
Closed Form Expression ◽  
Proportional Reinsurance ◽  
Insurance Company ◽  
Risky Assets ◽  
Price Of Risk

AbstractIn this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations.

scholarly journals OPTIMAL INVESTMENT AND REINSURANCE IN A JUMP DIFFUSION RISK MODEL

2011 ◽  
Vol 52 (3) ◽  
pp. 250-262 ◽  
Author(s):  
XIANG LIN ◽  
PENG YANG
Keyword(s):  
Risk Model ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Risk Process ◽  
Proportional Reinsurance ◽  
Insurance Company ◽  
Closed Form Solutions ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

AbstractWe consider an insurance company whose surplus is governed by a jump diffusion risk process. The insurance company can purchase proportional reinsurance for claims and invest its surplus in a risk-free asset and a risky asset whose return follows a jump diffusion process. Our main goal is to find an optimal investment and proportional reinsurance policy which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton–Jacobi–Bellman equation, closed-form solutions for the value function as well as the optimal investment and proportional reinsurance policy are obtained. We also discuss the effects of parameters on the optimal investment and proportional reinsurance policy by numerical calculations.

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