The Optimal Control Of Guarantees

Market economy is a credit economy. Credit risk, as a risk that may bring much harm to the financial market, not only has an impact on the proper functioning of enterprises at the micro level, but also influences the socio-economic order at the macro level. Starting late, China's market economy requires much assurance in the distempered financial system and environment in which the market entity has trouble in information, interest, faith and unbalanced rights and duties in the unsmooth market trading. In order to satisfy the need of various market entities to shift the credit risk, assurance is widely applied in financial agreements and also provides an important conceptual framework for credit analysis. Assurance is the promise made by the warrantor to the creditor that the warrantor itself will pay off the debt for the debtor or discharge the debt with particular property under the circumstance that the debtor fails to do so. As the offspring of insufficient credit of market economy, assurance is adopted to increase the credit level of the debtor and balance the information amount between the creditor and the debtor, and consequently to decrease the transaction cost and improve the market system. With the evolution of financial liberalization and innovation, the warrantor's demand for the assurance risk control has emerged, especially after the 2008 global financial crisis, which shows the importance of doing related research on assurance risks. Since the essence of modern financial theories includes two major subjects, risk management and utility optimization, this thesis attempts to apply the utility optimization theory to risk management. Optimal control refers to the acquiring of a control strategy by which the system can reach the optimal state (max/min) of the given objective function under a certain constraint condition. Since the validity of the historical statistics may be influenced by the uncertain deviation, the validity of assurance, according to the optimal control theory, is determined by the realization of the optimal supervision and control. Taking the credit risk controlling cost of assurance as the subject of research, this thesis attempts to simplify the controlling problem via numerical calculation by building models based on the optimal control theory and the random process of asset value. Different from the previous study, the research approach of this thesis will produce a framework in a broad sense, rather than a specific framework. Simultaneously, the mathematical method that is not widely used in financial research will be adopted in this thesis.The structure of the thesis is as follows:Firstly, the connotation of the optimal control theory is reviewed.Secondly, referring to the optimal control theory and related credit assurance pricing theories home and abroad, this study builds up the dynamic process and takes the cost minimization strategy as the objective function. In this model the asset value's random process has also been taken into consideration. We assume that the objective of the warrantor is to control the credit risk cost and the assurance cost in process of time. The instantaneous cost is marked as f ( y(t),t), and the variable cost f ( y(t),t)is determined by the asset value y(t). But this phase can not precisely indicate the instantaneous cost of the credit risk, nor can the total cost be produced. The objective function can only be precisely defined according to the credit risk pricing literature mentioned above.Thirdly, according to the attainability of information, the issue can be divided into two cases, observation with complete information and that with incomplete information, each being discussed respectively. Due to the complexity of the study, only the first case of assurance risk controlling is studied in the thesis, and the market value of asset is adopted. In such case, both the warrantor and the credit risk exposure are able to know the asset value at any time (t). The bidding of assurance is decided according to the asset value. As for the second case, the result can be acquired on the basis of complete information.Fourthly, controlling is defined as the pulse process decided by the risk bearer (i.e. the side who undertakes the responsibility of credit risk exposure) according to the dynamic process of secured asset. As any risk loan is the combination of riskless contract and assurance, the application of pulse theory in the analysis of optimal control allows the uses of pulse control in the assurance duration. Then, the analog simulation is achieved through related software. Based on the results, the factors that determine the control decision making are analyzed.Last but not least, any form of defaulting may indicate the existence of recessive assurance. Since no deposit assurance policy has been pushed in China, the Chinese government actually offers recessive assurance for the debts of banks. In terms of government's financial risk control, the government's recessive assurance for banks is taken as an example to analyze the optimal control.Based on the analysis above, the conclusions are drawn as follows:First, the analog analysis of the optimal control model of assurance risk has proved the rationality of the research method. The application of this method in the study of government's recessive assurance risk control has proved the feasibility of the method. Based on the assumption, we can get an optimal program group to solve the controlling problem: in the first stage, the minimum cost of assurance risk is confirmed; in the second stage, the optimal path to reach the minimum cost is confirmed. The advantage of this method lies in that it can clarify the cost controlling process of credit control, which enables policy-makers to make a choice between undertaking a risk and paying controlling cost. As this method is a preliminary attempt to apply the optimal control theory to the credit risk analysis, the study in this thesis has been carried out on the basis of a few hypotheses and simplified procedures, and to some extent it may not fit into the realistic condition. Therefore the expanded study of the method may be challenging.