Stochastic Analysis & Mathematical Finance Seminars

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.

Past events in this series
15 June 2020
16:00
Mykhaylo Shkolnikov

Further Information: 

[Meeting URL removed for security reasons]

Abstract

 

Abstract: The calibration problem for local stochastic volatility models leads to two-dimensional stochastic differential equations of McKean-Vlasov type. In these equations, the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. While such equations enjoy frequent application in the financial industry, their mathematical analysis poses a major challenge. I will explain how to prove the strong existence of stationary solutions for these equations, as well as the strong uniqueness in an important special case. Based on joint work with Daniel Lacker and Jiacheng Zhang.  
 

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  • Stochastic Analysis & Mathematical Finance Seminars
22 June 2020
16:00
Abstract

Most of the basic results on martingale problems extend to the setting in which the generator depends on a control.  The “control” could represent a random environment, or the generator could specify a classical stochastic control problem.  The equivalence between the martingale problem and forward equation (obtained by taking expectations of the martingales) provides the tools for extending linear programming methods introduced by Manne in the context of controlled finite Markov chains to general Markov stochastic control problems.  The controlled martingale problem can also be applied to the study of constrained Markov processes (e.g., reflecting diffusions), the boundary process being treated as a control.  The talk includes joint work with Richard Stockbridge and with Cristina Costantini. 

  • Stochastic Analysis & Mathematical Finance Seminars
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