An Optimal Stopping Problem for Jump Diffusion Logistic Population Model

Mathematical Problems in Engineering ◽

10.1155/2016/5839672 ◽

2016 ◽

Vol 2016 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Yang Sun ◽

Xiaohui Ai

Keyword(s):

Optimal Stopping ◽

Critical State ◽

Explicit Solution ◽

Population Model ◽

Value Function ◽

Jump Diffusion ◽

Optimal Value Function ◽

Optimal Stopping Problem ◽

Optimal Value ◽

Poisson Jump

This paper examines an optimal stopping problem for the stochastic (Wiener-Poisson) jump diffusion logistic population model. We present an explicit solution to an optimal stopping problem of the stochastic (Wiener-Poisson) jump diffusion logistic population model by applying the smooth pasting technique (Dayanik and Karatzas, 2003; Dixit, 1993). We formulate this as an optimal stopping problem of maximizing the expected reward. We express the critical state of the optimal stopping region and the optimal value function explicitly.

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Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

Abstract and Applied Analysis ◽

10.1155/2014/194962 ◽

2014 ◽

Vol 2014 ◽

pp. 1-19 ◽

Cited By ~ 3

Author(s):

De-Lei Sheng ◽

Ximin Rong ◽

Hui Zhao

Keyword(s):

Optimal Control ◽

Control Strategy ◽

Value Function ◽

Asset Price ◽

Jump Diffusion ◽

Risk Process ◽

Hjb Equation ◽

Optimal Value Function ◽

Optimal Control Strategy ◽

Optimal Value

This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV) model. It aims at obtaining the explicit optimal control strategy and the optimal value function. Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB) equation is established. Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motionsW(t)andW1(t). A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem. Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealthxand decreasing with the volatility rate of risk asset price. However, the optimal value functionV(t;x;s)is increasing with the appreciation rateμof risk asset.

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