Study On Models Of Control And Optimization Of Investment Decision Under Uncertainty

The contradiction between the demand and the scarce of resources obliges people to make decisions to meet their demand as much as possible with limited resources. For individuals, in order to realize the optimal demand of consumption, they face the decision-making problem of consumption and investment; for enterprises, in order to get the optimal reward from investment, they have to settle decision-making problem of many aspects, and inevitably those financial policies are made under the condition of uncertainty. In this paper these decision-making problems are to be studied with the method of stochastic optimal control. The studies on these decision-making problems are of great theoretical and practical significance in the probing of the operational mechanism of financial and economic system.Individual's optimal decision of consumption and investment is indeed composed of two parts: (1) consumption-saving decision, i.e. individuals have to decide how much income and wealth should be saved for future consumption; (2) portfolio decision, i.e. individuals should make a decision on how to distribute their savings among those opportunities that can be used to make wealth grow and to make them consume more in the future. Normally the two aspects of the decision are correlated and cannot be made independently. R.C.Merton first studied it with the model of individual's optimal consumption and portfolio decision in continuous time. Now in the perfect and complete financial market, the basic researches in this kind of decision-making problem have been abundant. However, the real market is imperfect and incomplete. Since 1980s and 1990s the decision-making problems of optimal consumption and investment have been studying in succession. Because of the great increase of the complexity and difficulty, advance is little in the problem, very few important achievements have been achieved and it remains a topic of general interest in the international financial field. It is one of this paper's primary content to generalize the classical Merton Model, and with the optimized models such progresses have been made in this paper as followed:By studying a stochastic optimal control model about the expected utility maxim of constant absolute risk aversion utility on infinite time horizon, the effect of non-negativity constraint of consumption on the optimal decision of consumption and investment is studied in detail. With the application of Cox-Huang method that is based on martingale representation technology, the optimal feedback control policies of the model in explicit formula and the analytic solution to level of key wealth are extracted.By contrasting we draw a conclusion that the optimum decision on consumption under the condition of non-negativity constraint will not make investors run the risk of bankruptcy; that the proportion of optimum consumption to the wealth decreases and the investors should adopt a more conservative investment strategy; and that when wealth becomes sufficiently great, the optimum decision under the condition of non-constraint is asymptotically valid.After considering the consumption and investment decision-making problem of the investor with constant relative risk aversion utility, a stochastic optimal control model of expected utility maxim on finite time horizon is set up. In the research, it is found that no matter what constant investment opportunity set he faces, the constraint of no borrowing is restrictive to those individuals with a lower level of risk aversion, hi this paper, with the application of stochastic optimal control theory, HJB equation and stochastic analysis technology, the analytical optimal feedback control policies on consumption and investment in two kinds of markets have been got and the further research of quantitative analysis has been made. The decrease of investor's optimal expected utility with the constraint of no borrowing is proved rigorously in theory. The result shows that, whether or not there is the constraint of no borrowing, the prospect of security m...