بهینه منابع مالی و سود سهام کنترل از شرکت بیمه با هزینه های مبادله ثابت و متناسب

We consider the optimal financing and dividend control problem of the insurance company with fixed and proportional transaction costs. The management of the company controls the reinsurance rate, dividends payout as well as the equity issuance process to maximize the expected present value of the dividends payout minus the equity issuance until the time of bankruptcy. This is the first time that the financing process in an insurance model with two kinds of transaction costs, which come from real financial market has been considered. We solve the mixed classical-impulse control problem by constructing two categories of suboptimal models, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance.

In this paper, we consider an insurance company with the fixed and the proportional transaction costs. In this model the management controls the dividends payout, equity issuance and the risk exposure by proportional reinsurance policy. We study the value of the company via the expected present value of the dividends payout minus the equity issuance. This is a mixed classical-impulse control on diffusion models. Diffusion models for companies that control their risk exposure by means of dividends payout have attracted a lot of interests recently. We refer the readers to He and Liang (2007) and the references therein. Optimizing dividends payout is a classical problem starting from the early work of Borch, 1969 and Borch, 1967 and Gerber (1972). For some applications of control theory in insurance mathematics, see, Harrison and Taksar (1983), Højgaard and Taksar, 1998a and Højgaard and Taksar, 1998b, Martin-Löf (1983), Asmussen and Taksar (1997) and Cadenillas et al. (2006). A survey can be found in Taksar (2000). However, there are very few results concerned with the equity issuance of the insurance company. In the real financial market, equity issuance is an important approach for the insurance company to earn profit and reduce risk. Harrison and Taksar (1983) consider the optimal control problem with a lower and an upper reflecting barrier. Sethi and Taksar (2002) recently considered the model for the company that can control its risk exposure by issuing new equity as well as paying dividends. He and Liang (2007) work out the optimal financing and dividend control problem of the insurance company without the fixed transaction costs. In this paper, we consider both the fixed and the proportional transaction costs incurred by the equity issuance. The amount of money paid by the shareholder is K+β2ξ,β2>1K+β2ξ,β2>1, to meet the equity issuance of ξξ. KK is the fixed transaction costs generated by the advisory and consulting fees, β2β2 is the proportional transaction costs generated by the tax. We assume that if the company pays ll as dividends, the shareholder can get β1l,β1<1β1l,β1<1, and we can omit the fixed transaction costs in the dividends payout process because the financial system is operated with an ever increasing efficiency and the dividends payout processes seldom generate fixed transaction costs. We refer the reader to Cadenillas et al. (2006), which consider the optimal dividends policy of the insurance company with the fixed and proportional transaction costs, and without the equity issuance. Motivated by the work of He and Liang (2007), Harrison and Taksar (1983) and Sethi and Taksar (2002), we can consider the equity issuance and dividends payout as the absorbing and reflecting boundaries of the reserve process, respectively. We will deal with the mixed classical-impulse control problem by using the line of He and Liang (2007). We expect our results would be of interest for theory of mixed classical-impulse control. The paper is organized as follows: In Section 2, we establish the control model of the insurance company with fixed and proportional transaction costs. In Section 3, we present some mathematical results proved by He and Liang (2007) for proving the main results of this paper. In Section 4, we construct solutions of two categories of suboptimal models. One is the classical model without equity issuance, the other never goes bankrupt by equity issuance. uct solutions of two categories of suboptimal models. In Section 5, we identify the value function and the optimal strategy with the corresponding solution in either category of suboptimal models, depending on the relationships between the coefficients. We give the conclusion of this paper in Section 6.

In this paper, we consider the optimal control problem of the insurance company with both the fixed and proportional transaction costs. The management of the company controls the reinsurance rate, dividends payout and the equity issuance to maximize the expected present value of the dividends payout minustheequityissuancebeforebankruptcy.Tobemorerealistic, weassumetheequityissuanceprocessesincurboththefixedand theproportionaltransactioncosts.Theformeraregeneratedbythe advisory and consulting fees as well as the latter are generated by the tax. This is the first time that the financing process in an insurance model with the fixed transaction costs has been considered,andwefinallyfindthatitactsasabsorbingorreflecting boundary of the reserve process. In order to find the solution of mixed classical-impulse control problem. We construct two categoriesofsuboptimalmodels,oneistheclassicalmodelwithout equityissuance,theothernevergoesbankruptbyequityissuance. At last, we identify the value function and the optimal strategy withthecorrespondingsolutionineithercategoryofsuboptimal models,dependingontherelationshipsbetweenthecoefficients.