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Optimal Dividend-Equity Issuance Strategy in a Dual Model with fixed and Proportional transaction costs

Acta Mathematicae Applicatae Sinica 2015年第2期31卷 405-426页

作者： Shu-min CHEN Zhong-fei LI School of Management Guangdong University of Technology Sun Yat-sen Business School Research Center for Financial Engineering and Risk Management Sun Yat-sen University

In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy,which is defined as the first time when the company＇s capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems： one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity *** first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company＇s reserve above zero by issuing new equity, depending on the model＇s parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.

关键词： dual risk model fixed transaction cost optimal dividend strategy optimal equity issuance strategy mixed impulse-singular control

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Optimal Dividend Payout for Classical Risk Model with Risk Constraint

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 721-734页

作者： Shu-min CHEN School of Management Guangdong University of Technology

In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.

关键词： optimal dividend risk constraint classical risk model fixed transaction cost

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