Ӧ�ø���ͳ�� 2013, 29(2) 136-150 DOI:      ISSN: 1001-4268 CN: 31-1256

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Optimal Dividend Payments in a Dual Risk Model with both Fixed and Proportional Costs
Chen Shumin,He Chunxiong
School of Mathematics and and Information Sciences, Zhaoqing University, School of Automation, Guangdong University
of Technology, School of Sciences, South China University of Technology
Abstract:

In this paper, we study the optimal dividend
problem in a dual risk model, which might be appropriate for
companies that have fixed expenses and occasional profits. Assuming
that dividend payments are subject to both proportional and fixed
transaction costs, our object is to maximize the expected present
value of dividend payments until ruin, which is defined as the first
time the company's surplus becomes negative. This optimization
problem is formulated as a stochastic impulse control problem. By
solving the corresponding quasi-variational inequality (QVI), we
obtain the analytical solutions of the value function and its
corresponding optimal dividend strategy when jump sizes are
exponentially distributed.

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