Volume 25, Issue 2
Dividend Maximization when Cash Reserves Follow a Jump-Diffusion Process

Lili Li, Jinghai Feng & Lixin Song

Commun. Math. Res., 25 (2009), pp. 143-158.

Published online: 2021-06

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  • Abstract

This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends paid out until the time of ruin. Under concavity assumption on the optimal value function, the paper states some general properties and, in particular, smoothness results on the optimal value function, whose analysis mainly relies on viscosity solutions of the associated Hamilton-Jacobi-Bellman (HJB) equations. Based on these properties, the explicit expression of the optimal value function is obtained. And some numerical calculations are presented as the application of the results.

  • Keywords

jump-diffusion model, dividend payment, Hamilton-Jacobi-Bellman equation, viscosity solution.

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-143, author = {Li , Lili and Feng , Jinghai and Song , Lixin}, title = {Dividend Maximization when Cash Reserves Follow a Jump-Diffusion Process}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {2}, pages = {143--158}, abstract = {

This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends paid out until the time of ruin. Under concavity assumption on the optimal value function, the paper states some general properties and, in particular, smoothness results on the optimal value function, whose analysis mainly relies on viscosity solutions of the associated Hamilton-Jacobi-Bellman (HJB) equations. Based on these properties, the explicit expression of the optimal value function is obtained. And some numerical calculations are presented as the application of the results.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19301.html} }
TY - JOUR T1 - Dividend Maximization when Cash Reserves Follow a Jump-Diffusion Process AU - Li , Lili AU - Feng , Jinghai AU - Song , Lixin JO - Communications in Mathematical Research VL - 2 SP - 143 EP - 158 PY - 2021 DA - 2021/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19301.html KW - jump-diffusion model, dividend payment, Hamilton-Jacobi-Bellman equation, viscosity solution. AB -

This paper deals with the dividend optimization problem for an insurance company, whose surplus follows a jump-diffusion process. The objective of the company is to maximize the expected total discounted dividends paid out until the time of ruin. Under concavity assumption on the optimal value function, the paper states some general properties and, in particular, smoothness results on the optimal value function, whose analysis mainly relies on viscosity solutions of the associated Hamilton-Jacobi-Bellman (HJB) equations. Based on these properties, the explicit expression of the optimal value function is obtained. And some numerical calculations are presented as the application of the results.

LiliLi, JinghaiFeng & LixinSong. (2021). Dividend Maximization when Cash Reserves Follow a Jump-Diffusion Process. Communications in Mathematical Research . 25 (2). 143-158. doi:
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