scholarly journals Optimal Reinsurance Strategy for an Insurer and a Reinsurer with Generalized Variance Premium Principle

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Danping Li ◽  
Chaohai Shen
Keyword(s):  
Regularization Parameter ◽  
Risk Process ◽  
Model Parameters ◽  
Value Functions ◽  
Optimal Reinsurance ◽  
Terminal Wealth ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Optimal Value Functions

This paper focuses on the optimal reinsurance problem with consideration of joint interests of an insurer and a reinsurer. In our model, the risk process is assumed to follow a Brownian motion with drift. The insurer can transfer the risk to the reinsurer via proportional reinsurance, and the reinsurance premium is calculated according to the variance and standard deviation premium principles. The objective is to maximize the expected exponential utility of the weighted sum of the insurer’s and the reinsurer’s terminal wealth, where the weight can be viewed as a regularization parameter to measure the importance of each party. By applying stochastic control theory, we establish the Hamilton–Jacobi–Bellman equation and obtain explicit expressions of optimal reinsurance strategies and optimal value functions. Furthermore, we provide some numerical simulations to illustrate the effects of model parameters on the optimal reinsurance strategies.

scholarly journals Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

Dynamic admission control for loss systems with batch arrivals

2005 ◽  
Vol 37 (04) ◽  
pp. 915-937 ◽  
Author(s):  
E. L. Örmeci ◽  
A. Burnetas
Keyword(s):  
Admission Control ◽  
Sufficient Conditions ◽  
Monotonicity Property ◽  
Value Functions ◽  
Single Class ◽  
Batch Arrivals ◽  
Optimal Value ◽  
Service Rates ◽  
Definition Of ◽  
Optimal Value Functions

We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches; each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of a ‘preferred class’ for systems receiving mixed and single-class batches separately, and derive sufficient conditions for each system to have a preferred class. We also establish a monotonicity property of the optimal value functions, which reduces the number of possibly optimal actions.

scholarly journals Explicit Solution of Reinsurance-Investment Problem for an Insurer with Dynamic Income under Vasicek Model

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
De-Lei Sheng
Keyword(s):  
Explicit Solution ◽  
Bellman Equation ◽  
Control Technique ◽  
Power Utility ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman Equation ◽  
Interest Rate Model ◽  
Hamilton Jacobi Bellman

Unlike traditionally used reserves models, this paper focuses on a reserve process with dynamic income to study the reinsurance-investment problem for an insurer under Vasicek stochastic interest rate model. The insurer’s dynamic income is given by the remainder after a dynamic reward budget being subtracted from the insurer’s net premium which is calculated according to expected premium principle. Applying stochastic control technique, a Hamilton-Jacobi-Bellman equation is established and the explicit solution is obtained under the objective of maximizing the insurer’s power utility of terminal wealth. Some economic interpretations of the obtained results are explained in detail. In addition, numerical analysis and several graphics are given to illustrate our results more meticulous.

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