scholarly journals Impulse Control of Proportional Reinsurance with Constraints

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Hui Meng ◽  
Tak Kuen Siu
Keyword(s):  
Optimal Control ◽  
Diffusion Process ◽  
Impulse Control ◽  
Dividend Policy ◽  
Proportional Reinsurance ◽  
Value Functions ◽  
Insurance Company ◽  
Control Policies

We consider an insurance company whose surplus follows a diffusion process with proportional reinsurance and impulse dividend control. Our objective is to maximize expected discounted dividend payouts to shareholders of the company until the time of bankruptcy. To meet some essential requirements of solvency control (e.g., bankruptcy not soon), we impose some constraints on the insurance company's dividend policy. Under two types of constraints, we derive the value functions and optimal control policies of the company.

Control Strategy of Proportional Reinsurance with Dividend Process

2014 ◽  
Vol 488-489 ◽  
pp. 1301-1305
Author(s):  
Shi Liang Sun ◽  
Xiao Qian Huang ◽  
Lu Lian
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Control Strategy ◽  
Proportional Reinsurance ◽  
Insurance Company ◽  
Optimal Control Strategy ◽  
Return Function ◽  
Existence Of Optimal Control

This paper is concerned with the problem of proportional reinsurance control strategy with dividend process in insurance company. The existence of optimal control strategy is proved by variational inequality,and the specific construct of optimal control strategy and the explicit structure of optimal return function are derived.

scholarly journals Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

2020 ◽  
Vol 2020 ◽  
pp. 1-26 ◽  
Author(s):  
Man Li ◽  
Yingchun Deng ◽  
Ya Huang ◽  
Hui Ou
Keyword(s):  
Diffusion Process ◽  
Default Risk ◽  
Optimal Strategies ◽  
Jump Diffusion ◽  
Corporate Bond ◽  
Value Functions ◽  
Case Scenario ◽  
Worst Case ◽  
Special Cases ◽  
Jump Diffusion Model

In this paper, we consider a robust optimal investment-reinsurance problem with a default risk. The ambiguity-averse insurer (AAI) may carry out transactions on a risk-free asset, a stock, and a defaultable corporate bond. The stock’s price is described by a jump-diffusion process, and both the jump intensity and the distribution of jump amplitude are uncertain, i.e., the jump is ambiguous. The AAI’s surplus process is assumed to follow an approximate diffusion process. In particular, the reinsurance premium is calculated according to the generalized mean-variance premium principle, and the reinsurance type has to follow a self-reinsurance function. In performing dynamic programming, both the predefault case and the postdefault case are analyzed, and the optimal strategies and the corresponding value functions are derived under the worst-case scenario. Moreover, we give a detailed proof of the verification theorem and give some special cases and numerical examples to illustrate our theoretical results.

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