Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Motivated by the problem of calibrating linear pricing rules to the market prices of Asian options, we provide a new weak uniqueness result for degenerate diffusions. In particular, we consider path-dependent stochastic differential equations where the diffusion coefficient is a function of both the current location of the process and the running integral of the process, and we show that uniqueness holds for continuous, strictly positive-definite diffusion coefficients. These results combine tools from the theory of singular integrals on Lie groups with the localization machinery of Stroock and Varadhan.

Speaker: Gerard Brunick, University of Texas at Austin

Slides: (TBA)