ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

Chuancun Yin · Yuzhen Wen · Yongxia Zhao

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Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

Abstract

Abstract In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

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References

2005Stochastic Integration and Differential Equations 1997Controlled diffusion models for optimal dividend pay-out 1995Optimization of the flow of dividends 1999Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example 2006Optimal dividends in the dual model 1998Introduction to Stochastic Calculus with Applications 2010Smoothness of scale functions for spectrally negative Lévy processes 2013Optimal dividend problem with a terminal value for spectrally positive Lévy processes

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2014Optimal dividend problems for a jump-diffusion model with captial injections and proportional transaction costs 2018Spectrally negative Lévy risk model under Erlangized barrier strategy

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