Minicourse: Topics on defaultable market and on default valuation, Part 2

The word "market" designates any framework in which financial contracts are settled down. A market in which defaultable securities are traded will be called a defaultable market. In this lecture we try to draw the profile of a general theory of defaultable market and of default valuation. Along the line of this general theory, we present a series of topics, which illustrate the recent advances in the directions of the modeling based on the enlargement of filtration, the default computation, the arbitrage analysis of default modeling, etc..
The lecture will be organized in five parts : a short introduction, a presentation of the theory of enlargement of filtration in connection with the default modeling, a discussion on the mathematical representation of default market, an arbitrage analysis of default modeling, a conclusion section with the invariance measure. Mathematical results will be rigourously presented with their exact setup and statements. However, the corresponding proofs will be usually omitted, replaced by the original references.