Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model

2013 ◽  
Vol 53 (3) ◽  
pp. 504-514 ◽  
Author(s):  
Hui Zhao ◽  
Ximin Rong ◽  
Yonggan Zhao
Keyword(s):  
Jump Diffusion ◽  
Risk Process ◽  
Heston Model ◽  
Investment Problem

scholarly journals Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with Delay and Dependent Risks

2019 ◽  
Vol 2019 ◽  
pp. 1-21
Author(s):  
Yan Zhang ◽  
Peibiao Zhao
Keyword(s):  
Investment Strategy ◽  
Risky Asset ◽  
Exponential Utility ◽  
Heston Model ◽  
Verification Theorem ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Dependent Risks ◽  
Insurance Business ◽  
Explicit Expressions

This paper investigates a robust optimal excess-of-loss reinsurance and investment problem with delay and dependent risks for an ambiguity-averse insurer (AAI). The AAI’s wealth process is assumed to be two dependent classes of insurance business. He/she can purchase excess-of-loss reinsurance from the reinsurer and invest in a risk-free asset and a risky asset whose price follows Heston model. We obtain the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy by maximizing the expected exponential utility of AAI’s terminal wealth. Finally, we give the proof of the verification theorem. Our models and results posed here can be regarded as a generalization of the existing results in the literature.

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 LONG MEMORY VERSION OF STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL WITH STOCHASTIC INTENSITY

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Somayeh Fallah ◽  
Farshid Mehrdoust
Keyword(s):  
Stochastic Volatility ◽  
Long Range ◽  
Diffusion Model ◽  
Long Memory ◽  
Stock Price ◽  
Real Data ◽  
Jump Diffusion ◽  
Heston Model ◽  
Long Range Dependence ◽  
Jump Diffusion Model

It is widely accepted that certain financial data exhibit long range dependence. We consider a fractional stochastic volatility jump diffusion model in which the stock price follows a double exponential jump diffusion process with volatility described by a long memory stochastic process and intensity rate expressed by an ordinary Cox, Ingersoll, and Ross (CIR) process. By calibrating the model with real data, we examine the performance of the model and also, we illustrate the role of long range dependence property by comparing our presented model with the Heston model.

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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