On the optimality of Periodic barrier strategies for a spectrally positive Lévy process

Abstract

We study the optimal dividend problem in the dual model where dividend payments can only be made at the jump times of an independent Poisson process. In this context, Avanzi et al. [5] solved the case with i.i.d. hyperexponential jumps; they showed the optimality of a (periodic) barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level. In this paper, we generalize the results for a general spectrally positive Levy process with additional terminal payoff/penalty at ruin, and also solve the case with classical bail-outs so that the surplus is restricted to be nonnegative. The optimal strategies as well as the value functions are concisely written in terms of the scale function. Numerical results are also given.

To appear on Insurance: Mathematics and Economics

References in corpus (2)

• On the optimal dividend problem for a spectrally negative Lévy process
• Spectrally negative Lévy processes with Parisian reflection below and classical reflection above

Cited by in corpus (3)

• The $W,Z$ scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends
• On the optimality of joint periodic and extraordinary dividend strategies
• Non-zero-sum optimal stopping game with continuous versus periodic exercise opportunities