Time-based approach, pricing models

In order to solve the probability of default, reduced-form models adopt a different approach. They are mainly based on debt prices rather than equity prices. In fact, they do not take into account the fundamentals of the firm and the default event is determined as an exogenous process without considering the underlying asset movements. In addition, the models are mainly based oti X t), that is the default intensity as a function of time. In particular, these models use the decomposition of the risky rate (risk-free rate and risk premium) in order to determine the default probabilities, recovery rates and debt values. Although structural models have the advantage to foUow a reliable measure of credit risk, that is the firm value, reduced-form approach overcomes the Umitatimi in which the balance sheet is not the unique indicator of the default prediction. 

Model Predictive Control (MPC) has been also appUed to SC problems as a reactive approach. MPC is a control sfiategy based on the explicit use of a process model to predict the process performance over a period of time (Camacho and Bordons 1995). The model attempts to predict the control variables for a set of time periods. Predicted confiol variables depend on disturbance forecasts (i.e., demand, prices, and interest rates) and also on a set of given parameters that are known as control inputs. The MPC algorithm attempts to optimize a performance criterion that is a function of the control variables. Only a portion of the control variables, the portion corresponding to the following time period, is applied to the system. Next, as new control input information and disturbance forecasts are collected, the whole procedure is repeated, which produces a feed-forward effect and enables the system to counteract the environment dynamics. The procedure is illustrated in Fig. 1.6. 

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