# Optimal Dividend and Proportional Reinsurance Strategy Under Standard Deviation Premium Principle

Optimal Dividend and Proportional Reinsurance Strategy Under Standard Deviation Premium Principle This paper investigates the optimal dividend and proportional reinsurance problem. The reinsurance premium principle is calculated by the standard deviation premium principle rather than the expected value premium principle. The objective is to maximize the discounted value of accumulated dividend payments. Two cases are discussed here to solve this optimization problem, based on whether there is a restriction on the dividend rate or not. Closed-form expressions for the value function and optimal dividend and reinsurance policies are obtained for both cases. Finally, numerical examples are given to describe the effect of the parameters on the value function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

# Optimal Dividend and Proportional Reinsurance Strategy Under Standard Deviation Premium Principle

, Volume 45 (2) – Mar 1, 2022
20 pages      /lp/springer-journals/optimal-dividend-and-proportional-reinsurance-strategy-under-standard-YQ4N01vEL0
Publisher
Springer Journals
Copyright © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-021-01220-w
Publisher site
See Article on Publisher Site

### Abstract

This paper investigates the optimal dividend and proportional reinsurance problem. The reinsurance premium principle is calculated by the standard deviation premium principle rather than the expected value premium principle. The objective is to maximize the discounted value of accumulated dividend payments. Two cases are discussed here to solve this optimization problem, based on whether there is a restriction on the dividend rate or not. Closed-form expressions for the value function and optimal dividend and reinsurance policies are obtained for both cases. Finally, numerical examples are given to describe the effect of the parameters on the value function.

### Journal

Bulletin of the Malaysian Mathematical Sciences SocietySpringer Journals

Published: Mar 1, 2022

Keywords: Standard deviation premium principle; Stochastic control; Dividend optimization; Proportion reinsurance; Optimal strategy; Hamilton–Jacobi–Bellman equation; 60J99; 91G05

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