This Week in Mathematics


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Entries for this week: 4

Wednesday March 10, 2021

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Thursday March 11, 2021

Financial Mathematics Seminar [url]
Set-valued martingales and backward stochastic differential equations
- Cagin Ararat, Bilkent University
Time: 3:05pm Room: fsu.zoom.us/j/97820191506
Abstract/Desc: Motivated by the connection between univariate dynamic risk measures and backward stochastic differential equations, we start building a theory for set-valued backward stochastic differential equations (SV-BSDE). As a first attempt in this direction, we formulate a simple SV-BSDE with a compact-valued driver function and study the well-posedness of this SV-BSDE. A key point in establishing well-posedness is the availability of an integral representation for set-valued martingales. We prove a new martingale representation theorem which allows the initial value of the martingale to be nontrivial, which is in contrast to the available literature. Joint work with Jin Ma (USC) and Wenqian Wu (USC).

Friday March 12, 2021

Colloquium Tea
Time: 3:00 pm Room: 204 LOV

Colloquium [url]
Recent advances in rough volatility
- Antoine Jacquier, Imperial College London
Time: 3:05pm Room: Zoom
Abstract/Desc: Rough volatility models are one the new “hot topics” in Quantitative Finance (its creators, Jim Gatheral and Mathieu Rosenbaum having just been named Risk Quant of the Year!!). They rely on the delicate observation that the instantaneous volatility of asset prices (Equity stocks, indices, commodities, …) is driven by a process featuring characteristics similar to those of a fractional Brownian motion with short memory. This surprising discovery gave rise to a plethora of papers (an exhaustive review of which is available at https://sites.google.com/site/roughvol/home). Nothing comes for free though and this new modelling paradigm initially suffered from the complexity of introducing non-Markovian dynamics, whereby classical tools ( among which Feynman-Kac PDE formulation of Markovian systems, Monte Carlo schemes) need a fresh facelift. In this context, we introduce a wide variety of new tools and see how they all come together to the rescue, in particular: Large and moderate deviations for non-Markovian systems Deep learning techniques for path-dependent PDEs We shall endeavour to strike a fair balance between technical tools, immediate applications and modelling intuitions.

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Department of Mathematics

This Week in Mathematics