# Optimal dividend strategy in compound binomial model with bounded dividend rates

Optimal dividend strategy in compound binomial model with bounded dividend rates We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Optimal dividend strategy in compound binomial model with bounded dividend rates

, Volume 30 (4) – Nov 6, 2014
12 pages      /lp/springer-journals/optimal-dividend-strategy-in-compound-binomial-model-with-bounded-2Tvppd043d
Publisher
Springer Journals
Copyright © 2014 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-014-0428-2
Publisher site
See Article on Publisher Site

### Abstract

We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 6, 2014

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