A0624
Title: Sensitivity of robust optimization problems with ambiguity on semimartingale differential characteristics
Authors: Daniel Bartl - University of Vienna (Austria)
Ariel Neufeld - Nanyang Technological University (Singapore)
Kyunghyun Park - Nanyang Technological University (Singapore) [presenting]
Abstract: A sensitivity analysis is provided for robust optimization problems, where model ambiguity is captured by a closed ball (with respect to some suitable norms) around each semimartingale differential characteristic of a postulated reference Ito-semimartingale. Assuming a decision maker seeks to derive a robust control such that its stochastic integral optimizes her minimax value function, the first-order correction, which is defined as the first-order derivative of the minimax value function with respect to the radius of the ball at 0, is obtained. In particular, the correction is characterized in terms of the optimizer of the value function under the postulated reference semimartingale without model ambiguity and the gradient of the function at the optimum. The approach relies on dual norm representations and the tools of backward stochastic differential equations. In the context of finance and economics, some possible applications and extensions are discussed within the proposed results.
