Before the 2008 financial crisis, most research in financial mathematics focused on pricing derivatives without considering the effects of counter parties' default, illiquidity problems, and the role of the repurchase agreement (Repo) market. In our research, we apply an alternating renewal process to describe the switching between different financial regimes and develop a framework for pricing a European claim. The price is characterized as a solution to a backward stochastic differential equation (BSDE), and we prove the existence and uniqueness of this solution. In a numerical study based on a deep learning algorithm for BSDEs, we compare the effect of different parameters on the valuation of it.
My name is Weijie Pang, and I am a postdoctoral fellow in mathematics with a research area in stochastic analysis and financial mathematics at McMaster University. In 2019, I obtained my Ph.D. degree in mathematics under the advisement of Professor Stephan Sturm at Worcester Polytechnic Institute (WPI). I have been teaching courses, related to probability, statistics, differential equations and programming, both online and on-campus sections. I am also working in diverse projects, such as financial derivatives' pricing, banking strategies, economic analysis, and pandemic modeling.
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