This chapter studies structural and reduced-form credit risk models under incomplete information using techniques from stochastic filtering. We start with a brief introduction to stochastic filtering. Next we cover the pricing of corporate securities (debt and equity) in structural models under partial information. Furthermore we study the construction of a dynamic reduced-form credit risk mode...

Filtering problems with general exponential quadratic criteria are investigated for Gauss-Markov processes. In this setting, the Linear Exponential Gaussian and Risk-Sensitive filtering problems are solved and it is shown that they may have different solutions.

This paper considers robust filtering for a nominal Gaussian state-space model, when an incremental relative entropy tolerance is applied to each dynamical model component. The problem is formulated as a dynamic minimax game which is shown to admit a saddle point. The structure of the saddle point is characterized by applying and extending results presented earlier in [1] for static least-squar...

This paper considers the measurement of the equity risk premium in financial markets. While there exists a vast amount of research into its behaviour, particularly in US markets, this is largely based on regression based techniques which do not capture well the dynamic and forward looking nature of the risk premium. In this paper the time variation of the unobserved risk premium is modelled by ...

Merton’s model views equity as a call option on the asset of the firm. Thus the asset is partially observed through the equity. Then using nonlinear filtering an explicit expression for likelihood ratio for underlying parameters in terms of the nonlinear filter is obtained. As the evolution of the filter itself depends on the parameters in question, this does not permit direct maximum likelihoo...

background: butterworth, gaussian, hamming, hanning, and parzen are commonly used spect filters during filtered back-projection (fbp) reconstruction, which greatly affect the quality and size accuracy of image. materials and methods: this study involved a cardiac phantom in which 1.10 cm thick cold defect was inserted into its myocardium wall and filled with 4.0 μci/ml (0.148 mbq/ml) 99mtc conc...