Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy
Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy
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DOI：
10.1088/1469-7688/4/3/007
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发表时间：
2004-06
影响因子：
1.3
通讯作者：
Bjarne Højgaard;M. Taksar
中科院分区：
文献类型：
--
作者：
Bjarne Højgaard;M. Taksar
本文提出了一个企业风险管理模型，企业通过选择不同的经营活动来控制风险和潜在利润，并可选择将其储备投资于由无风险资产（债券）和风险资产（股票）组成的金融市场。我们考虑的例子是一个大公司，如保险公司，其流动资产在没有控制和投资的情况下，作为布朗运动波动，具有恒定的正漂移和恒定的扩散系数。我们将扩散系数解释为风险暴露，而漂移与潜在利润相关。在每一个时刻，都有一个减少风险敞口的选择，同时减少潜在的利润，比如为保险公司与另一家保险公司使用比例再保险。该公司将其储备投资于金融市场，该市场由经典的布莱克-斯科尔斯模型描述。公司管理层还控制着向股东支付的股息。目标是找到一个政策，包括投资策略，风险控制和股息分配方案，使最大限度地提高预期的总折扣股息支付到破产的时间。我们应用受控扩散理论来解决这个问题，并证明了存在一个水平u1>0，使得最优行动是将所有超过u1的准备金作为股息进行分配。此外，存在一个常数x 0，其中x 0 <u1，使得风险暴露在（0，x 0）上从零单调增加到可能的最大值。投资的最优选择取决于风险的市场价格[image omitted]，其中r 0，r1分别表示债券和股票的平均收益率，σP表示股票价格的波动率。我们得到以下结果。(1)mp≤0：投资于债券。(2)MP很大：把所有的钱都投资在股票上。(3)MP很小：存在x 0 <x1<u1，使得当当前准备金x小于x 0时，投资于股票的准备金的最优比例是常数，当准备金水平超过x1时，投资于股票的准备金的最优比例是x在[x 0，x1]上的增函数。
This paper represents a model for risk management in a firm which exercises control of its risk as well as potential profit by choosing different business activities among those available to it. Furthermore, the firm has an option of investing its reserve in a financial market consisting of a risk-free asset (bond) and a risky asset (stock). The example we consider is that of a large corporation such as an insurance company, whose liquid assets in the absence of control and investments fluctuate as a Brownian motion with a constant positive drift and a constant diffusion coefficient. We interpret the diffusion coefficient as risk exposure, while drift is associated with potential profit. At each moment of time there is an option to reduce risk exposure, simultaneously reducing the potential profit, like using proportional reinsurance with another carrier for an insurance company. The company invests its reserve in a financial market, which is described by a classical Black-Scholes model. The management of the company also controls the dividend pay-outs to shareholders. The objective is to find a policy, consisting of investment strategy, risk control and dividend distribution scheme, which maximizes the expected total discounted dividends paid out until the time of bankruptcy. We apply the theory of controlled diffusions to solve the problem and show that there is a level u1>0 such that the optimal action is to distribute all the reserve in excess of u1 as dividends. Furthermore, there exists a constant x0, with x0<u1, such that the risk exposure monotonically increases on (0, x0) from zero to the maximum possible. The optimal choice of investments depends on the market price of risk [image omitted] , where r0, r1 denotes the mean rate of return of bond and stock respectively and σP denotes the volatility of the stock price. We get the following results. (1) mp≤0: invest everything in bond. (2) mp is large: invest everything in stock. (3) mp is small: there exists x0<x1<u1, such that the optimal fraction of the reserve invested in stock is constant when the current reserve x is less than x0 and it is an increasing function of x on [x0, x1] with all the reserve to be invested in stock whenever the reserve level exceeds x1.