Robust Methods in Financial Mathematics and Stochastic Control

Faculty-development competitive research grants program for 2020-2022 (batch 2)

Starting with the pioneering works the models describing random movements in finance are constructed with respect to a fixed probability measure that is estimated statistically from historical data of the underlying dynamics. These models are then evaluated with respect to expected value performance criteria. However, in many practical problems the expected value criteria may not be appropriate to measure performance. In particular, when the model takes risk into consideration, that is to say when the model is risk averse, the performance of the model can be evaluated in different methods. A classical approach is representing the risk averseness of the model by utility functions, which satisfy certain regularity principles. The second approach is based on the assumption that it is impossible to precisely identify the models of the underlying dynamics. Hence, it assumes there is a model ambiguity, also called Knightian uncertainty, intrinsically in the problem. In that regard, each scenario corresponds to a probability distribution, and the agent in the model takes a robust approach by considering these scenarios simultaneously.