scholarly journals Optimal investment and proportional reinsurance for a jump–diffusion risk model with constrained control variables

2016 ◽  
Vol 296 ◽  
pp. 443-461 ◽  
Author(s):  
Ya Huang ◽  
Xiangqun Yang ◽  
Jieming Zhou
Keyword(s):  
Risk Model ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Proportional Reinsurance ◽  
Constrained Control ◽  
Control Variables

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.

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 Robust equilibrium investment and reinsurance strategy with bounded memory and common shock dependence

2021 ◽  
Author(s):  
Sheng Li
Keyword(s):  
Control Theory ◽  
Stochastic Control ◽  
Risk Model ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Optimal Decision ◽  
Stochastic Control Theory ◽  
Bounded Memory ◽  
Jump Diffusion Model ◽  
Robust Equilibrium

In this paper, we consider the robust investment and reinsurance problem with bounded memory and risk co-shocks under a jump-diffusion risk model. The insurer is assumed to be ambiguity-averse and make the optimal decision under the mean-variance criterion. The insurance market is described by two-dimensional dependent claims while the risky asset is depicted by the jump-diffusion model. By introducing the performance in the past, we derive the wealth process depicted by a stochastic delay differential equation (SDDE). Applying the stochastic control theory under the game-theoretic framework, together with stochastic control theory with delay, the robust equilibrium investment-reinsurance strategy and the corresponding robust equilibrium value function are derived. Furthermore, some numerical examples are provided to illustrate the effect of market parameters on the optimal investment and reinsurance strategy.

Robust Optimal Investment-Reinsurance Strategies for a Jump-Diffusion Risk Model with Mean-reverting Stock Return

2021 ◽  
Vol 7 (6) ◽  
pp. 6100-6114
Author(s):  
Wu Yungao
Keyword(s):  
Financial Market ◽  
Stock Return ◽  
Value Function ◽  
Risk Model ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Insurance Companies ◽  
Insurance Company ◽  
Terminal Time ◽  
The Value Function

Objectives: This paper proposes a strategy of robust optimal investment reinsurance for insurance companies. It was assumed that the surplus procedure of the insurance company satisfies the jump-diffusion procedure. Insurance companies could invest their surplus funds in the financial market consisted of both risk assets and one risk-free asset. The price procedure of risk assets satisfies the stochastic procedure with a mean reversion rate. Considering the uncertainty of the model, the ambiguity-averse insurance firm aims to enhance the exponential utility of insurance surplus at terminal time. This paper has investigated the problem of robust optimal investment reinsurance and obtained the differential equation supported by the value function.

scholarly journals Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Yan Li ◽  
Guoxin Liu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Optimal Strategies ◽  
Proportional Reinsurance ◽  
Two Dimensional ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Poisson Risk Model

We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.

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