Stochastic Analysis 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.

Past events in this series
20 November 2017
14:15
VLAD MARGARINT
Abstract

In this talk, I am going to report on some on-going research at the interface between Rough Paths Theory and Schramm-Loewner evolutions (SLE). In this project, we try to adapt techniques from Rough Differential Equations to the study of the Loewner Differential Equation. The main ideas concern the restart of the backward Loewner differential equation from the singularity in the upper half plane. I am going to describe some general tools that we developed in the last months that lead to a better understanding of the dynamics in the closed upper half plane under the backward Loewner flow.
Joint work with Prof. Dmitry Belyaev and Prof. Terry Lyons

  • Stochastic Analysis Seminar
20 November 2017
15:45
ANDREY KORMILITZIN
Abstract

Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. The signature method is derived from stochastic analysis (rough paths theory) and has the ability to capture important properties of complex ordered time series data. To explore whether the onset of episodes of mania and depression can be identified using self-reported mood data.

  • Stochastic Analysis Seminar
27 November 2017
14:15
GECHUN LIANG
Abstract

In this talk, we will discuss about some recent results of optimal investment problems and related backward stochastic differential equations (BSDE).

In the first part, we will solve utility maximization with (unbounded) random endowments by using the tools from quadratic BSDE with unbounded terminal data. This will in turn solve a long-term outstanding problem about utility indifference valuation of unbounded payoffs (e.g. call options). Joint work with Ying Hu and Shanjian Tang.  

In the second part, we will present a new class of dynamic utilities, called forward performance criteria, firstly introduced by Musiela and Zariphopoulou. We will show how they can be constructed by using ergodic BSDE and infinite horizon BSDE. As an application, we will study the large maturity behavior of (forward) entropic risk measures. Joint work with Alfred Chong, Ying Hu and Thaleia Zariphopoulou.

  • Stochastic Analysis Seminar
27 November 2017
15:45
ALEKSANDAR MIJATOVIC
Abstract

Abstract: In this talk we describe an invariance principle for a class of non-homogeneous martingale random walks in $\RR^d$ that can be recurrent or transient for any dimension $d$. The scaling limit, which we construct, is a martingale diffusions with law determined uniquely by an SDE with discontinuous coefficients at the origin whose pathwise uniqueness may fail. The radial component of the diffusion is a Bessel process of dimension greater than 1. We characterize the law of the diffusion, which must start at the origin, via its excursions built around the Bessel process: each excursion has a generalized skew-product-type structure, in which the angular component spins at infinite speed at the start and finish of each excursion. Defining a Riemannian metric $g$ on the sphere $S^{d−1}$, different from the one induced by the ambient Euclidean space, allows us to give an explicit construction of the angular component (and hence of the entire skew-product decomposition) as a time-changed Browninan motion with drift on the Riemannian manifold $(S^{d−1}, g)$. In particular, this provides a multidimensional generalisation of the Pitman–Yor representation of the excursions of Bessel process with dimension between one and two. Furthermore, the density of the stationary law of the angular component with respect to the volume element of $g$ can be characterised by a linear PDE involving the Laplace–Beltrami operator and the divergence under the metric $g$. This is joint work with Nicholas Georgiou and Andrew Wade.

  • Stochastic Analysis Seminar
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