Malliavin calculus has been applied to several areas. In the first part of the talk, we focus on applications to mathematical finance. A brief review of classical applications, such as the calculation of Greeks will be provided. We then describe the exponential formula of Schellhorn et al., in several different models: Brownian, fractional Brownian, and Levy (Stochastic Processes and Applications, 2019). A recent formula for the pricing of options in Heston’s model will be discussed. We then switch to applications of Malliavin calculus to probability density estimates, following the seminal work of Nourdin and Viens (Electronic Journal of Probability 2009). We will present an extension of this method to Levy processes.

Henry Schellhorn is professor at the Institute of Mathematical Sciences at Claremont Graduate University, of which he is the current director. Henry’s current research areas include: stochastic analysis, mathematical finance, and traffic models, in particular the modelling of congestion pricing. Henry has been developing graduate courses at the cutting edge of the mathematical sciences, for instance stochastic partial differential equations, quantum computing, and several others. He has published in top-tier journals, including Management Science, Stochastic processes and Applications, and the European Journal of Operational Research. Before working in academia, professor Schellhorn worked in the decision software industry, first in Switzerland, and then in Los Angeles. Henry is an American and a Swiss citizen. He speaks French, and English, plays the piano, and enjoys the good life with his wife Malina and his two children.