Abstract
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.
Highlights
In the literatures of actuarial science and finance, the optimal dividend problem is one of the key topics
We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy
The problem of finding the optimal dividend strategy has become a popular topic in the actuarial literature
Summary
In the literatures of actuarial science and finance, the optimal dividend problem is one of the key topics. The pioneer work can be traced to de Finetti [1] who considered a discretetime risk model with step sizes ±1 and showed that a certain barrier strategy maximizes the expected discounted dividend payments. Inspired by the works of Avram et al [16], Loeffen [17], and Kyprianou et al [18], Yuen and Yin [26] considered the optimal dividend problem for a special Levy process with both upward and downward jumps and showed that the optimal strategy takes the form of a barrier strategy if the Levy measure (both negative and positive jumps) has a completely monotone density. Our main results show that the optimal dividend strategy is still of a barrier type if the Levy process has certain positive jumps and Levy density of negative jumps is completely monotone or log-convex.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
