Abstract

The purpose of this paper is to examine the dual model, where the surplus or equity of the company is equal to the initial surplus minus expenses, plus the amount of occasional gains. Here the gain amount is deemed as a compound Poisson process {S(t)}. Now the company pays dividends to its shareholders according to a barrier strategy: Whenever the surplus attains the level b, the “overflow” is paid out as dividends. The problem is to determine b*, the optimal level of the dividend barrier in order to maximize the expected present value of future dividends (until ruin). According to B.Avanzi et al., 2006, if the initial surplus is b*, such expected present value is equal to the drift of the surplus over the compound interest rate. We can also use Laplace transforms to determine b*. A variety of numerical examples are provided.

The problem of two companies' merger has been discussed by H.Gerber and S.Shiu, 2006. The key is to find a condition to guarantee the expected present value of future dividends after merger is higher than before. In other words, the merger is successful. A nice formula was provided by H.Gerber and S.Shiu, 2006 under a Wiener process. According to some numerical tests, such condition for Wiener process model is no more valid in dual model. Meanwhile, a rough condition is provided.

Index

1. The Model
2. The Barrier Strategy
3. Alternative Method
4. Numerical Examples I
5. The Merger of Two Companies
6. Numerical Examples II
7. Appendix