Optimal excess-of-loss reinsurance and investment problem with delay and jump–diffusion risk process under the CEV model

2018 ◽  
Vol 342 ◽  
pp. 317-336 ◽  
Author(s):  
Chunxiang A ◽  
Yongzeng Lai ◽  
Yi Shao
Keyword(s):  
Jump Diffusion ◽  
Risk Process ◽  
Cev Model ◽  
Investment Problem

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.

OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT PROBLEM WITH CONSTRAINTS ON RISK CONTROL IN A GENERAL JUMP-DIFFUSION FINANCIAL MARKET

2016 ◽  
Vol 57 (3) ◽  
pp. 352-368
Author(s):  
HUIMING ZHU ◽  
YA HUANG ◽  
JIEMING ZHOU ◽  
XIANGQUN YANG ◽  
CHAO DENG
Keyword(s):  
Diffusion Process ◽  
Closed Form ◽  
Financial Market ◽  
Optimal Strategies ◽  
Jump Diffusion ◽  
Model Parameters ◽  
Proportional Reinsurance ◽  
Investment Problem ◽  
Jump Diffusion Process ◽  
The Impact

We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer’s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies.

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