Thu, 23 May 2019

13:00 - 14:00
L4

Monotone Solutions to the Moral Hazard Problem

Hanqing Jin
((Oxford University))
Abstract

We investigate monotone solutions of the moral hazard problems without the monotone likelihood ratio property. The solutions are explicitly characterised by a concave envelope relaxation approach for a two-action model in which the principal is risk neutral or exhibits constant absolute risk aversion.  

Tue, 05 Feb 2019

12:45 - 13:30
C3

A Boundary Layer Analysis for the Initiation of Reactive Shear Bands

Robert Timms
((Oxford University))
Abstract

Unintended low energy thermal or mechanical stimuli can lead to the accidental ignition of explosive materials. During such events, described as ‘insults’ in the literature, ignition of the explosive is caused by localised regions of high temperature known as ‘hot spots’. We develop a model which helps us to understand how highly localised shear deformation, so-called shear banding, acts as a mechanism for hot spot generation. Through a boundary layer analysis, we give a deeper insight into how the additional self heating caused by chemical reactions affects the initiation and development of shear bands,  and highlight the key physical properties which control this process.

Thu, 07 Mar 2019

13:00 - 14:00
L4

Optimal execution with rough path signatures

Imanol Perez
((Oxford University))
Further Information


 

Abstract

We consider a well-studied optimal execution problem under little assumptions on the underlying midprice process. We do so by using signatures from rough path theory, that allows converting the original problem into a more computationally tractable problem. We include a few numerical experiments where we show that our methodology is able to retrieve the theoretical optimal execution speed for several problems studied in the literature, as well as some cases not included in the literatture. We also study some estensions of our framework to other settings.
 

Thu, 14 Feb 2019

13:00 - 14:00
L4

Pathwise functional portfolio generation and optimal transport

Micheal Monoyios
((Oxford University))
Further Information

We make precise a remarkable connection, first observed by Pal and Wong (2016) and further analysed in the doctoral thesis of Vervuurt (2016), between functionally generated investments and optimal transport, in a model-free discrete-time financial market. A functionally generated portfolio (FGP) computes the investment in each stock through the prism of the super-differential of the logarithm of a concave function (the generating function of the FGP) of the market weight vector. Such portfolios have been shown to outperform the market under suitable conditions. Here, in our pathwise discrete-time scenario, we equate the convex-analytic cyclical monotonicity property characterising super-differentials, with a $c$-cyclical monotonicity property of the unique Monge solution of an appropriately constructed optimal transport problem with cost function $c$, which transfers the market portfolio distribution to the FGP distribution. Using the super-differential characterisation of functional investments, we construct optimal transport problems for both traditional (multiplicative) FGPs, and an ``additive'' modification introduced by Karatzas and Ruf (2017), featuring the same cost function in both cases, which characterise the functional investment. In the multiplicative case, the construction differs from Pal and Wong (2016) and Vervuurt (2016), who used a ``multiplicative'' cyclical monotonicity property, as opposed to the classical cyclical monotonicity property used here.
  
We establish uniqueness of the solution to the relevant optimal transport problem, elevating the connection observed by Pal and Wong (2016) to an exact equivalence between optimal transport and functional generation. We explore ramifications, including pathwise discrete-time master equations for the evolution of the relative wealth of the investment when using the market portfolio as numeraire. We take the pathwise continuous time limit, assuming continuous paths which admit well-defined quadratic variation, to establish model-free continuous-time master equations for both types of functionally generated investment, providing an alternative derivation to the recent proof of Schied et al (2018) of the master equation for multiplicative FGPs, as well as an extension to the case of additive functionally generated trading strategies.

Thu, 08 Nov 2018

13:00 - 14:00
L4

Talks by graduate students

Donovan Platt and Yufei Zhang (DPhil students)
((Oxford University))
Abstract

Donovan Platt
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Economic Agent-Based Model Calibration

Interest in agent-based models of financial markets and the wider economy has increased consistently over the last few decades, in no small part due to their ability to reproduce a number of empirically-observed stylised facts that are not easily recovered by more traditional modelling approaches. Nevertheless, the agent-based modelling paradigm faces mounting criticism, focused particularly on the rigour of current validation and calibration practices, most of which remain qualitative and stylised fact-driven. While the literature on quantitative and data-driven approaches has seen significant expansion in recent years, most studies have focused on the introduction of new calibration methods that are neither benchmarked against existing alternatives nor rigorously tested in terms of the quality of the estimates they produce. We therefore compare a number of prominent ABM calibration methods, both established and novel, through a series of computational experiments in an attempt to determine the respective strengths and weaknesses of each approach and the overall quality of the resultant parameter estimates. We find that Bayesian estimation, though less popular in the literature, consistently outperforms frequentist, objective function-based approaches and results in reasonable parameter estimates in many contexts. Despite this, we also find that agent-based model calibration techniques require further development in order to definitively calibrate large-scale models.

Yufei Zhang
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A penalty scheme and policy iteration for stochastic hybrid control problems with nonlinear expectations

We propose a penalty method for mixed optimal stopping and control problems where the objective is evaluated
by a nonlinear expectation. The solution and free boundary of an associated HJB variational inequality are constructed from a sequence
of penalized equations, for which the penalization error is estimated. The penalized equation is then discretized by a class of semi-implicit
monotone approximations. We further propose an efficient iterative algorithm with local superlinear convergence for solving the discrete
equation. Numerical experiments are presented for an optimal investment problem under ambiguity to demonstrate the effectiveness of
the new schemes.  Finally, we extend the penalty schemes to solve stochastic hybrid control problems involving impulse controls.

Thu, 08 Mar 2018

17:15 - 18:15
L1

Alain Goriely - Can Mathematics Understand the Brain?

Alain Goriely
((Oxford University))
Abstract

Oxford Mathematics Public Lectures

Can Mathematics Understand the Brain?' - Alain Goriely

The human brain is the object of the ultimate intellectual egocentrism. It is also a source of endless scientific problems and an organ of such complexity that it is not clear that a mathematical approach is even possible, despite many attempts. 

In this talk Alain will use the brain to showcase how applied mathematics thrives on such challenges. Through mathematical modelling, we will see how we can gain insight into how the brain acquires its convoluted shape and what happens during trauma. We will also consider the dramatic but fascinating progression of neuro-degenerative diseases, and, eventually, hope to learn a bit about who we are before it is too late. 

Alain Goriely is Professor of Mathematical Modelling, University of Oxford and author of 'Applied Mathematics: A Very Short Introduction.'

March 8th, 5.15 pm-6.15pm, Mathematical Institute, Oxford

Please email @email to register

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