Convexity of ruin probability and optimal dividend strategies for a general Levy process

TL;DR

This paper investigates the convexity of ruin probability and identifies conditions under which barrier strategies are optimal for dividend payouts in companies modeled by general Levy processes.

Contribution

It establishes the convexity of ruin probability for Levy processes and characterizes when barrier strategies are optimal for dividend distribution.

Findings

Convexity of ruin probability under certain Levy process conditions

Optimal dividend strategy is a barrier strategy under specified conditions

Provides new theoretical insights using potential analysis of subordinators

Abstract

In this paper, we consider the optimal dividends problem for a company whose cash reserves follow a general Levy 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 appeal to very 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.