An Introduction to the Mathematical Theory of Credit Risk
主讲人: Philip Protter (Columbia University)
活动时间: 从 2020-05-12 13:00 到 2020-05-28 09:50
场地: 北京国际数学研究中心,全斋全29教室
Time: May 12, 19, 26 13:00-14:50
May 14, 21, 28 8:00-9:50
Ever since the 2008 financial catastrophe in the US Financial Markets (involving the failure of the ‘too-big-to-fail’ big banks of Baer Stearns and Lehmann Brothers, as well as the hidden failures of Merrill Lynch, Wachovia Bank, and the financial arm of General Motors which caused the near failure of General Motors itself) a lot of attention in the research community has focused on the theory of credit risk. A lot of the blame was attributed to complicated financial products and their incorrect credit ratings. Nevertheless, while there have been attempts at reforms, including the development of Credit Valuations Adjustments and the like, one suspects in fact that little has changed in the intervening eleven years.
We will present the mathematical theory of credit risk, beginning at the beginning with the theory of interest rates, and continuing with the Merton theory of structural default models. We will discuss also the weakness of such a theory, which then will segue into the reduced form theory of credit risk, a more modern alternative. This leads naturally to the theory of point processes and compensators. We will relate the usual implicit assumption of absolutely continuous paths of compensators to an underlying Markovian nature belying the theory. We will include a bit of the newly developing theory of CVX and the like, with its connections to backwards, and forward-backwards stochastic differential equations.
Prerequisites: A working knowledge of measure theoretic probability theory.