Thesis defence K.W. Chau: finance
Numerical Finance with Backward Stochastic Differential Equations. Promotor 1: Prof.dr.ir. C.W. Oosterlee (EWI);
In the financial market, a derivative is a contract whose payoff depends on the future performance of underlying financial assets. A classical technique to price these products is to construct a replicating portfolio. Such a portfolio consists of the underlying assets, mimics the value movement of the derivative, and matches the payoff whenever it is realized. This setting results in a stochastic dynamic equation for a random process and a terminal condition for said process. This type of system is called a backward stochastic differential equation (BSDE) and pricing derivative is one of the many applications of BSDE. There are also research interests of BSDE application in mathematical finance, optimization, numerical solution for partial differential equations and more, on top of the fundamental research on its mathematical properties.
The main aims of this thesis are to study various numerical schemes in the approximation of the occurring expectations and their applications in numerically solving BSDEs, as the unsolvability is one of the key hurdles of industrial application of BSDEs. We focus on numerical expectation/finite measure integration since the majority of the BSDE solvers consists of two parts, conditional expectations computations, and deterministic functions to map these expectations to target approximations. By varying the solvers for conditional expectations, we effectively generate various schemes for BSDEs that can suit different requirements. As such, our results not only provide effective algorithms to solve BSDEs but also contribute to the research in numerical integration too.
For access to theses by the PhD students you can have a look in TU Delft Repository, the digital storage of publications of TU Delft. Theses will be available within a few weeks after the actual thesis defence.