Past Mathematical Finance Internal Seminar

27 January 2017
13:00
Jan Obloj
Abstract


We pursue robust approach to pricing and hedging in mathematical
finance. We develop a general discrete time setting in which some
underlying assets and options are available for dynamic trading and a
further set of European options, possibly with varying maturities, is
available for static trading. We include in our setup modelling beliefs by
allowing to specify a set of paths to be considered, e.g.
super-replication of a contingent claim is required only for paths falling
in the given set. Our framework thus interpolates between
model-independent and model-specific settings and allows to quantify the
impact of making assumptions. We establish suitable FTAP and
Pricing-Hedging duality results which include as special cases previous
results of Acciaio et al. (2013), Burzoni et al. (2016) as well the
Dalang-Morton-Willinger theorem. Finally, we explain how to treat further
problems, such as insider trading (information quantification) or American
options pricing.
Based on joint works with Burzoni, Frittelli, Hou, Maggis; Aksamit, Deng and Tan.
 

  • Mathematical Finance Internal Seminar
2 December 2016
13:00
Christoph Reisinger
Abstract

In this talk, we present and analyse a class of “filtered” numerical schemes for second order Hamilton-Jacobi-Bellman (HJB) equations, with a focus on examples arising from stochastic control problems in financial engineering. We start by discussing more widely the difficulty in constructing compact and accurate approximations. The key obstacle is the requirement in the established convergence analysis of certain monotonicity properties of the schemes. We follow ideas in Oberman and Froese (2010) to introduce a suitable local modification of high order schemes, which are necessarily non-monotone, by “filtering” them with a monotone scheme. Thus, they can be proven to converge and still show an overall high order behaviour for smooth enough value functions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests. 

This talk is based on joint work with Olivier Bokanowski and Athena Picarelli.

  • Mathematical Finance Internal Seminar
18 November 2016
13:00
Zhenru Wang and Vadim Kaushansky
Abstract

Zhenru Wang
Title: Multi-Index Monte Carlo Estimators for a Class of Zakai SPDEs
Abstract:   
We first propose a space-time Multi-Index Monte Carlo (MIMC) estimator for a one-dimensional parabolic SPDE of Zakai type. We compare the computational cost required for a prescribed accuracy with the Multilevel Monte Carlo (MLMC) method of Giles and Reisinger (2012). Then we extend the estimator to a two-dimensional variant of SPDE. The theoretical analysis shows the benefit of using MIMC in high dimensional problems over MLMC methods. Numerical tests confirm these finding empirically.


Vadim Kaushansky
Title: An extended structural default model with jump risk
Abstact:
We consider a structural default model in an interconnected banking network as in Itkin and Lipton (2015), where there are mutual obligations between each pair of banks. We analyse the model numerically for the case of two banks with jumps in their asset value processes. Specifically, we develop a finite difference method for the resulting two-dimensional partial integro-differential equation, and study its stability and consistency. By applying this method, we compute joint and marginal survival probabilities, as well as prices of credit default swaps (CDS) and first-to-default swaps (FTD), Credit and Debt Value Adjustments (CVA and DVA).

 

  • Mathematical Finance Internal Seminar
4 November 2016
13:00
Tongseok Lim
Abstract

We will introduce variants of the optimal transport problem, namely martingale optimal transport problem and subharmonic martingale transport problem. Their motivation is partly from mathematical finance. We will see that in dimension greater than one, the additional constraints imply interesting and deep mathematical subtlety on the attainment of dual problem, and it also affects heavily on the geometry of optimal solutions. If time permits, we will introduce still another variant of the martingale transport problem, called the multi-martingale optimal transport problem.

  • Mathematical Finance Internal Seminar
21 October 2016
13:00
Abstract

In practice, stochastic decision problems are often based on statistical estimates of probabilities. We all know that statistical error may be significant, but it is often not so clear how to incorporate it into our decision making. In this informal talk, we will look at one approach to this problem, based on the theory of nonlinear expectations. We will consider the large-sample theory of these estimators, and also connections to `robust statistics' in the sense of Huber.

  • Mathematical Finance Internal Seminar
17 June 2016
13:00
to
14:30
Harald Oberhauser
Abstract

Mining massive amounts of sequentially ordered data and inferring structural properties is nowadays a standard task (in finance, etc). I will present some results that combine and extend ideas from rough paths and machine learning that allow to give a general non-parametric approach with strong theoretical guarantees. Joint works with F. Kiraly and T. Lyons.

  • Mathematical Finance Internal Seminar
10 June 2016
13:00
to
14:30
Abstract

Time inconsistency arises when one's preferences are not aligned
over time; thus time-inconsistent dynamic control is essentially
a self control problem. In this talk I will introduce several classes of time-inconsistent
dynamic optimisation problems together with their economic
motivations, and highlight the ways to address the time inconsistency.
I will then provide a solution to a continuous-time portfolio choice
model under the rank-dependent utility which is inherently time inconsistent.
  • Mathematical Finance Internal Seminar

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