Martingale method for optimal investment and proportional reinsurance

2021 ◽  
Vol 36 (1) ◽  
pp. 16-30
Author(s):  
Shuang-sui Liu ◽  
Wen-jing Guo ◽  
Xin-le Tong
Keyword(s):  
Optimal Investment ◽  
Proportional Reinsurance ◽  
Martingale Method

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 TRADING STRATEGY WITH PARTIAL INFORMATION AND THE VALUE OF INFORMATION: THE SIMPLIFIED AND GENERALIZED MODELS

2001 ◽  
Vol 04 (05) ◽  
pp. 759-772 ◽  
Author(s):  
ZHAOJUN YANG ◽  
CHAOQUN MA
Keyword(s):  
Value Of Information ◽  
Optimization Problem ◽  
Partial Information ◽  
Optimal Investment ◽  
General Situation ◽  
Martingale Method ◽  
Optimal Trading ◽  
Security Price ◽  
The Interest Rate ◽  
Optimal Investment And Consumption

In this paper we deal with the optimization problem of maximizing the expected total utility from consumption under the case of partial information. By means of the martingale method and filter theory, we have acquired an explicit solution to optimal investment and consumption determined by the security prices for a special security price process. Furthermore, we establish a simple formula for valuing information, provided that the utility function is logarithmic. In the end, we extend most of the conclusions to a general situation where both the interest rate and dispersion coefficient of risk security follow some stochastic processes.

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.

Sign in / Sign up

Export Citation Format

Share Document