Applied Modeling Techniques and Data Analysis 2

3New Dividend Strategies

We will consider two insurance models with dividend payments. The first one is the Cramér-Lundberg model with exponentially distributed claims. We will study a barrier dividend strategy with the Parisian implementation delay. This means that if the company surplus stays a prescribed time interval h above the barrier, the overshoot is immediately paid as dividend. The expected discounted dividends paid before the Parisian ruin are chosen as the objective function. Numerical results are provided. The second model is the dual Cramér-Lundberg model with exponentially distributed gains. Instead of barrier strategy, we deal with a threshold one, meaning that dividends are paid with a constant rate as long as the surplus stays above the threshold.

3.1. Introduction

Insurance has a long and interesting history. Methods for transferring or distributing risks were practiced by Chinese and Babylonian traders more than 3000 years BCE. Let us mention, for example, the Code of Hammurabi c. 1750 BCE, which dealt with maritime risks. Mutual societies, run by their members with no external shareholders to pay, were the first to appear. The next step is joint stock companies. This explains the two-fold nature of modern insurance companies. The primary task of a company is indemnification of policyholder claims. The secondary, but very important, task is dividend payments to shareholders.

It is well known that insurance models are of the input-output type. We have to ...