Optimal control of investment-reinsurance problem for an insurer with jump-diffusion risk process: independence of Brownian motions
type: Item
instance of: scholarly article
title: Optimal control of investment-reinsurance problem for an insurer with jump-diffusion risk process: independence of Brownian motions
zbMATH Open document ID: 1406.91206
DOI: 10.1155/2014/194962
author: Delei Sheng
author: Hui Zhao
author: Ximin Rong
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 motions \(W(t)\) and \(W_1(t)\). 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 wealth \(x\) and decreasing with the volatility rate of risk asset price. However, the optimal value function \(V(t; x; s)\) is increasing with the appreciation rate \(\mu\) of risk asset.
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 7021912
zbMATH Keywords: investment-reinsurance problem
zbMATH Keywords: optimal stochastic control
zbMATH Keywords: jump-diffusion risk process
Wikidata QID: Q59035953
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/194962
OpenAlex ID: W2161078437
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description: scientific article; zbMATH DE number 7021912