Past Mathematical Finance Internal Seminar

14 November 2013
13:00
Victor Fedyashov and Ruolong Chen
Abstract
\textbf{Victor Fedyashov} \newline \textbf{Title:} Ergodic BSDEs with jumps \newline \textbf{Abstract:} We study ergodic backward stochastic differential equations (EBSDEs) with jumps, where the forward dynamics are given by a non-autonomous (time-periodic coefficients) Ornstein-Uhlenbeck process with Lévy noise on a separable Hilbert space. We use coupling arguments to establish existence of a solution. We also prove uniqueness of the Markovian solution under certain growth conditions using recurrence of the above mentioned forward SDE. We then give applications of this theory to problems of risk-averse ergodic optimal control. \newline \textbf{Ruolong Chen} \newline \textbf{Title:} tba \newline \textbf{Abstract:}
  • Mathematical Finance Internal Seminar
31 October 2013
13:00
James Newbury and Zhaoxu Hou
Abstract
\textbf{James Newbury} \newline Title: Heavy traffic diffusion approximation of the limit order book in a one-sided reduced-form model. \newline Abstract: Motivated by a zero-intelligence approach, we try to capture the dynamics of the best bid (or best ask) queue in a heavy traffic setting, i.e when orders and cancellations are submitted at very high frequency. We first prove the weak convergence of the discrete-space best bid/ask queue to a jump-diffusion process. We then identify the limiting process as a regenerative elastic Brownian motion with drift and random jumps to the origin. \newline \textbf{Zhaoxu Hou} \newline Title: Robust Framework In Finance: Martingale Optimal Transport and Robust Hedging For Multiple Marginals In Continuous Time \newline Abstract: It is proved by Dolinsky and Soner that there is no duality gap between the robust hedging of path-dependent European Options and a martingale optimal problem for one marginal case. Motivated by their work and Mykland's idea of adding a prediction set of paths (i.e. super-replication of a contingent claim only required for paths falling in the prediction set), we try to achieve the same type of duality result in the setting of multiple marginals and a path constraint.
  • Mathematical Finance Internal Seminar
24 October 2013
13:00
Wei Wei and Julen Rotaetxe
Abstract
Wei Wei \newline Title: "Optimal Switching at Poisson Random Intervention Times" (joint work with Dr Gechun Liang) \newline Abstract: The paper introduces a new class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward stochastic differential equation system. The value function and the optimal switching strategy are characterized by the solution of the underlying switching system. In a Markovian setting, the paper gives a complete description of the structure of switching regions by means of the comparison principle. \newline Julen Rotaetxe \newline Title: Applicability of interpolation based finite difference method to problems in finance \newline Abstract: I will present the joint work with Christoph Reisinger on the applicability of a numerical scheme relying on finite differences and monotone interpolation to discretize linear and non-linear diffusion equations. We propose suitable transformations to the process modeling the underlying variable in order to overcome issues stemming from the width of the stencil near the boundaries of the discrete spatial domain. Numerical results would be given for typical diffusion models used in finance in both the linear and non-linear setting.
  • Mathematical Finance Internal Seminar
13 June 2013
13:00
Martin Gould
Abstract
More than half of the world's financial markets use a limit order book mechanism to facilitate trade. For markets where trade is conducted through a central counterparty, trading platforms disseminate the same information about the limit order book to all market participants in real time, and all market participants are able to trade with all others. By contrast, in markets that operate under bilateral trade agreements, market participants are only able to view the limit order book activity from their bilateral trading partners, and are unable to trade with the market participants with whom they do not possess a bilateral trade agreement. In this talk, I discuss the implications of such a market structure for price formation. I then introduce a simple model of such a market, which is able to reproduce several important empirical properties of traded price series. By identifying and matching several robust moment conditions to the empirical data, I make model-based inference about the network of bilateral trade partnerships in the market. I discuss the implications of these findings for market stability and suggest how the regulator might improve market conditions by implementing simple restrictions on how market participants form their bilateral trade agreements.
  • Mathematical Finance Internal Seminar
30 May 2013
13:00
Peng Hu
Abstract
The aim of this lecture is to give a general introduction to the interacting particle system and applications in finance, especially in the pricing of American options. We survey the main techniques and results on Snell envelope, and provide a general framework to analyse these numerical methods. New algorithms are introduced and analysed theoretically and numerically.
  • Mathematical Finance Internal Seminar

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