Optimal Dividend Payment in De Finetti Models: Survey and New Results and Strategies

Abstract

We consider optimal dividend payment under the constraint that the with-dividend ruin probability does not exceed a given value α. This is done in most simple discrete De Finetti models. We characterize the value function V(s,α) for initial surplus s of this problem, characterize the corresponding optimal dividend strategies, and present an algorithm for its computation. In an earlier solution to this problem, a Hamilton-Jacobi-Bellman equation for V(s,α) can be found which leads to its representation as the limit of a monotone iteration scheme. However, this scheme is too complex for numerical computations. Here, we introduce the class of two-barrier dividend strategies with the following property: when dividends are paid above a barrier B, i.e., a dividend of size 1 is paid when reaching B+1 from B, then we repeat this dividend payment until reaching a limit L for some 0≤L≤B. For these strategies we obtain explicit formulas for ruin probabilities and present values of dividend payments, as well as simplifications of the above iteration scheme. The results of numerical experiments show that the values V(s,α) obtained in earlier work can be improved, they are suboptimal.

Time-inconsistent view on a dividend problem with penalty

“…This approach goes back to [Hipp, 2003]. Recent results in this direction are presented in [Hipp, 2018b, Hipp, 2018a, Hipp, 2020 and in talk by Brandon Israel García Flores 1 . On a finite time horizon such a constraint dividend maximization problem is analysed in [Grandits, 2015].…”

Special Issue “Computational Finance and Risk Analysis in Insurance”

“…While Richman and Wüthrich (2020), Krah et al (2020) and Kremsner et al (2020) consider new applications of neural networks in finance and insurance, Leduc and Nurkanovic Hot (2020), Mickel and Neuenkirch (2021), and Wang and Korn (2020) deal with the use of efficient algorithms for simulating and pricing problems encountered in advanced SDE frameworks. Moreover, Desmettre et al (2020) and Hipp (2020) present solutions to pricing and dividend problems that require efficient numerical computations for explicit examples. Wang and Korn (2020) examine the problem of pricing an American game option with default possibility.…”