The objective of this research is to address issues of non-uniform information structure in financial markets. Specifically, this research focuses on the credit risk issue where a financial institution or a firm fails to honor a financial contract, for instance, a bond issuing company being unable to repay the agreed-upon amount of money at the bond's maturity date. The first step of the research is to develop appropriate mathematical models and measurements for the difference between partial information (held by ordinary investors) and complete information (known to the firm's management). The second step is to quantify how a varying knowledge of the firm affects the estimation of the firm's default. Evaluation methodology will also be developed for pricing corporate bonds using only limited public information of the firm. This methodology will also be exploited to study the dependence among the default of multiple firms. Finally, several mathematical models will be suggested and explored for estimating the appropriate percentage to pay off for corporate bond holders in the event of the firm's default. A successful completion of the project will contribute to the theory of filtration, general theory of Markov processes, and stochastic filtering. It will hopefully lead to a better understanding and prediction of defaults, more efficient pricings for credit derivatives with the incorporation of different information structures, and consequently a more rational and efficient (credit) market
