Study Of Enterprise Investment, Dividend Decisions Under The Incomplete Information

With the rapid development of the economy in our country, enterprises have gradually strengthened their senses of the rational operations. As for choosing the operations policies, each step is concerned with the decision-making issue. Many scholars have studied the problem of the enterprise operation decisions. However, some problems still remain to be studied further. The literatures on the enterprise operation decisions have more studied the model under the condition of the internal factors rather than that of the external factor. While the economy is rapidly developing in the world, the external factors have some effect on the enterprise operation decisions and sometimes have decisive effect on the enterprise operation decisions. As the most important part of the enterprise operation decisions, the investment and dividend decisions together with some problems related to the investment and dividend decisions such as the merchant network and the ruin probability have been further studied by introducing both the internal variable and the external variable in this paper. The main points of this paper is as follows:A model of the investment-finance game with the internal variable and the external variable respect to the profits allocation between the enterprise and the investors is formulated. The optimal financing decision that the enterprise attracts the investors is obtained. The optimal decision shows that when the external variable is added to the contract by the enterprise, the investors accept the additional condition of the contract.The enterprise's portfolio model in which the profits of the investment along the proper lines is stochastic volatility and is affected by the external factor—price index is formulated (The enterprise's portfolio differs from the portfolio in the finance-mathematics , the enterprise's portfolio is actually referred to as the enterprise's developing blue picture in future ). The partial differential equation (P.D.E) which is met by the value function is transferred to be a semi-linear parabolic equation by using exponential transformation. The existence of continuous solution of the obtained equa-tion is verified, and the optimal portfolio decision is obtained. The effect of the external factor—price index on the (optimal) portfolio decision is shown. The applications of the exponential transformation technique in the portfolio are illustrated.? A model of the perturbed system of the enterprise's return is formulated in the case that the optimal portfolio is known and the external factor is perturbation. A stopping function which meets the extreme value function(EVE) is obtained by maximizing the investment income ratio. The existence of both the viscosity solution of the EVE and the optimal size of the enterprise investment corresponding to the viscosity solution is verified. An example shows the ununiqueness and the interval of the optimal investment size.? An algorithm of solving the (merchant) network reliability optimal path is proposed based on the cross-entropy. A degenerated matrix, which has only a single element equals unity and the remaining elements are zeros in each row, is obtained by using the finite step iteration of the auxiliary transition probability matrix, moreover, the optimal path is uniquely defined by the unity element of each row of the degenerated matrix. The numerical example shows that the (merchant) network optimization algorithm converges with very high probability to the optimal path.? A special investment model—a advertising model of the enterprise is formulated in the marketing system whose price of the merchandise is volatility. The obtained Bellman P.D.E is converted to a quadratic equation by using the exponential transformation. Moreover, the existence of smooth solution of the quadratic equation is verified. The optimal advertising decision is obtained based on the quadratic equation. Consequentially, the optimal advertising decision is obtained based on the complete information, by comparing it may be found that the enterprise's optimal advertising decision on the conditions of the complete information and incomplete information is different under the influence of various factors. The external factor-price has significantly effect on the optimal advertising decision in the case of incomplete information, while the external factor has no effecton the optimal advertising decision in the case of complete information.? A risk management model of the enterprise dividend with internal volatility and external impact is formulated. According to the optimality principle, the P.D.E which make the expected present value of the shareholder dividend maximizing is obtained. Both the analytical solution of the P.D.E and the optimal control policy is obtained by analyzing the obtained P.D.E. Two concepts of the "most tolerance loss" and the "critical ruin probability" are proposed, a new method of ruin probability of the enterprise is obtained, moreover, both the critical ruin probability and the cause of ruin probability of the different enterprises are obtained. The numerical example shows that the investment income of the different enterprises is positively proportion to the risk taken on by the enterprise.