- Mathematical Finance Internal Seminar
Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.
In this talk I will present two recent findings concerning the preconditioning of elliptic problems. The first result concerns preconditioning of elliptic problems with variable coefficient K by an inverse Laplacian. Here we show that there is a close relationship between the eigenvalues of the preconditioned system and K.
The second results concern the problem on mixed form where K approaches zero. Here, we show a uniform inf-sup condition and corresponding robust preconditioning.
- Computational Mathematics and Applications Seminar
- Mathematical Biology and Ecology Seminar
In semimartingale optimal transport problem, the functional to be minimized can be considered as a “stochastic action”, which is the expectationof a “stochastic Lagrangian” in terms of differential semimartingale characteristics. Therefore it would be natural to apply variational calculus approach to characterize the minimizers. R. Lassalle and A.B. Cruzeiro have used this approach to establish a stochastic Euler-Lagrangian condition for semimartingale optimal transport by perturbing the drift terms. Motivated by their work, we want to perform the same type of calculus for martingale optimal transport problem. In particular, instead of only considering perturbations in the drift terms, we try to find a nice variational family for volatility,and then obtain the stochastic Euler-Lagrangian condition for martingale laws. In the first part of this talk we will mention some basic results regarding the existence of minimizers in semimartingale optimal transport problem. In the second part, we will introduce Lassalle and Cruzeiro’s work, and give a simple example related to this topic, where the variational family is induced by time-changes; and then we will introduce some potential problems that are needed to be solved.
- Stochastic Analysis Seminar