Past Mathematical Finance Internal Seminar

7 November 2014
13:00
Gonçalo Simões and Vladimirs Murevics
Abstract

1. Minimising Regret in Portfolio Optimisation (Simões)

When looking for an "optimal" portfolio the traditional approach is to either try to minimise risk or maximise profit. While this approach is probably correct for someone investing their own wealth, usually traders and fund managers have other concerns. They are often assessed taking into account others' performance, and so their decisions are molded by that. We will present a model for this decision making process and try to find our own "optimal" portfolio.

2. Systemic risk in financial networks (Murevics)

Abstract: In this paper I present a framework for studying systemic risk and financial contagion in interbank networks. The current financial health of institutions is expressed through an abstract measure of robustness, and the evolution of robustness in time is described through a system of stochastic differential equations. Using this model I then study how the structure of the interbank lending network affects the spread of financial contagion through different contagion channels and compare the results for different network structures. Finally I outline the future directions for developing this model.

  • Mathematical Finance Internal Seminar
31 October 2014
13:00
Matthieu Mariapragassam and Siyuan Li
Abstract

1. Calibration and Pricing of Financial Derivatives using Forward PDEs (Mariapragassam)

Nowadays, various calibration techniques are in use in the financial industry and the exact re-pricing of call options is a must-have standard. However, practitioners are increasingly interested in taking into account the quotes of other derivatives as well.
We describe our approach to the calibration of a specific Local-Stochastic volatility model proposed by the FX group at BNP Paribas. We believe that forward PDEs are powerful tools as they allow to achieve stable and fast best-fit routines. We will expose our current results on this matter.

Joint work with Prof. Christoph Reisinger

2. Infinite discrete-time investment and consumption problem (Li)

We study the investment and consumption problem in infinite discrete-time framework. In our problem setting, we do not need the wealth process to be positive at any time point. We first analyze the time-consistent case and give the convergence of value function for infinite-horizon problem by value functions of finite-horizon problems.

Then we discuss the time-consistent case, and hope the value functions of finite-horizon problems will still converge to the infinite-horizon problem.

  • Mathematical Finance Internal Seminar
24 October 2014
13:00
Andrei Cozma and Hendrik J Brackmann
Abstract

1. A Hybrid Monte-Carlo Partial Differential Solver for Stochastic  Volatility Models (Cozma)

In finance, Monte-Carlo and Finite Difference methods are the most popular approaches for pricing options. If the underlying asset is modeled by a multidimensional system of stochastic differential equations, an analytic solution is rarely available and working under a given computational budget comes at the cost of accuracy. The mixed Monte-Carlo partial differential solver introduced by Loeper and Pironneau (2009) is one way to overcome this issue and we investigate it thoroughly for a number of stochastic volatility models. Our main concern is to provide a rigorous mathematical proof of the convergence of the hybrid method under different frameworks, which in turn justifies the use of Monte-Carlo simulations to compute the expected discounted payoff of the financial derivative. Then, we carry out a quantitative assessment based on a European call option by comparison with alternative numerical methods.

2. tbc (Brackmann)

 

  • Mathematical Finance Internal Seminar
6 June 2014
13:00
Ning Wang
Abstract
We are dwelling in the Big Data age. The diversity of the uses of Big Data unleashes limitless possibilities. Many people are talking about ways to use Big Data to track the collective human behaviours, monitor electoral popularity, and predict financial fluctuations in stock markets, etc. Big Data reveals both challenges and opportunities, which are not only related to technology but also to human itself. This talk will cover various current topics and trends in Big Data research. The speaker will share his relevant experiences on how to use analytics tools to obtain key metrics on online social networks, as well as present the challenges of Big Data analytics. Bio: Ning Wang (Ph.D) works as Researcher at the Oxford Internet Institute. His research is driven by a deep interest in analysing a wide range of sociotechnical problems by exploiting Big Data approaches, with the hope that this work could contribute to the intersection of social behavior and computational systems.
  • Mathematical Finance Internal Seminar
30 May 2014
13:00
Ning Wang
Abstract
We are dwelling in the Big Data age. The diversity of the uses of Big Data unleashes limitless possibilities. Many people are talking about ways to use Big Data to track the collective human behaviours, monitor electoral popularity, and predict financial fluctuations in stock markets, etc. Big Data reveals both challenges and opportunities, which are not only related to technology but also to human itself. This talk will cover various current topics and trends in Big Data research. The speaker will share his relevant experiences on how to use analytics tools to obtain key metrics on online social networks, as well as present the challenges of Big Data analytics. \\ Bio: Ning Wang (Ph.D) works as Researcher at the Oxford Internet Institute. His research is driven by a deep interest in analysing a wide range of sociotechnical problems by exploiting Big Data approaches, with the hope that this work could contribute to the intersection of social behavior and computational systems.
  • Mathematical Finance Internal Seminar
9 May 2014
13:00
Owen Jones
Abstract
Traditional diffusion models for random phenomena have paths with Holder regularity just greater than 1/2 almost surely but there are situations arising in finance and telecommunications where it is natural to look for models in which the Holder regularity of the paths can vary. Such processes are called multifractal and we will construct a class of such processes on R using ideas from branching processes. Using connections with multitype branching random walk we will be able to compute the multifractal spectrum which captures the variability in the Holder regularity. In addition, if we observe one of our processes at a fixed resolution then we obtain a finite Markov representation, which allows efficient simulation. As an application, we fit the model to some AUD-USD exchange rate data. Joint work with Geoffrey Decrouez and Ben Hambly
  • Mathematical Finance Internal Seminar
14 March 2014
13:00
Harald Oberhauser
Abstract
The question of how to derive useful bounds on arbitrage-free prices of exotic options given only prices of liquidly traded products like European call und put options has received much interest in recent years. It also led to new insights about classic problems in probability theory like the Skorokhod embedding problem. I will take this as a starting point and show how this progress can be used to give new results on general Monte-Carlo schemes.
  • Mathematical Finance Internal Seminar

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