# 2016-17 London Mathematical Finance Seminar Series

## The seminar is partially supported by INTECH.

Date: Thursday 6 October 2016

Speaker: Lukasz Szpruch, University of Edinburgh

Time: 17:00-18:00

Place: University College London - Physics Building A1/3, Gower Place, London, United Kingdom

Multilevel Monte Carlo for McKean-Vlasov SDEs

Stochastic Interacting Particle System (SIPS) and they limiting stochastic McKean-Vlasov equations offer a very rich and versatile modelling framework. On one hand, interactions allow to capture complex dependent structure, on the other provide a great challenge for Monte Carlo simulations. The non-linear dependence of the approximation bias on the statistical error renders classical variance reduction techniques not applicable. In this talk, we will propose a strategy to overcome this difficulty. In particular,  we will establish Multilevel Monte Carlo estimator for SIPS and demonstrate its computational superiority over standard Monte Carlo techniques.

Speaker:Mikko Pakkanen, Imperial College London

Time: 18:00-19:00

Place: University College London - Physics Building A1/3, Gower Place, London, United Kingdom

Modelling and forecasting rough volatility

In their recent, yet already seminal paper ("Volatility is rough", arXiv:1410.3394) Jim Gatheral, Thibault Jaisson, and Mathieu Rosenbaum argued that financial market volatility should be modelled by stochastic processes that are rougher than Brownian motion. In my talk, I will first present some new corroborative empirical evidence of the roughness of volatility, drawn from high-frequency data on more than five thousand assets. I will then introduce a new stochastic volatility model, building on the so-called Brownian semistationary (BSS) process, which is able to conveniently capture both the roughness and highly persistent long-term behaviour of volatility. Finally, I will discuss two parsimonious parameterisations of the BSS model and demonstrate their remarkable performance in volatility forecasting.

Joint work with Mikkel Bennedsen and Asger Lunde.

Date: Thursday 20 October 2016

Speaker: Christoph Reisinger, University of Oxford

Time: 17:00-18:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

High-order filtered schemes for time-dependent second order HJB equations

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.

Speaker: Pietro Siorpaes, Imperial College London

Time: 18:00-19:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

The Martingale Polar Sets

Martingale optimal transport (MOT) is a variant of the classical optimal transport problem where a martingale constraint is imposed on the coupling. In a recent paper, Beiglböck, Nutz and Touzi show that in dimension one there is no duality gap and that the dual problem admits an optimizer. A key step towards this achievement is the characterization of the polar sets of the family of all martingale couplings. Here we extend this characterization to arbitrary finite dimension through a deeper study of the convex order.

Date: Thursday 3 November 2016

Speaker: Ales Cerny, CASS Business School

Time: 18:00-19:00

Place: University College London - Physics Building A1/3, Gower Place, London, United Kingdom

Optimal trade execution under endogenous pressure to liquidate: theory and numerical solutions

We study optimal liquidation of a large trading position in a market with a temporary price impact. The novelty in our approach is that we endogenize the pressure to liquidate and hence allow the time horizon of liquidation to be determined endogenously, as part of the optimal strategy. The corresponding HJB equation leads to a severely singular initial value problem whose numerical solution we also study. In contrast to much of the existing literature spreading the liquidation strategy over a longer horizon is not necessarily beneficial to the trader.

Joint work with Pavol Brunovsky and Jan Komadel.

Speaker: Antoine Jacquier, Imperial College London

Time: 17:00-18:00

Place: University College London - Physics Building A1/3, Gower Place, London, United Kingdom

Some recent results on (asymptotics of) fractional volatility models

Date: Thursday 17 November 2016

Speaker: Chris Rogers, University of Cambridge

Time: 17:00-18:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

High-frequency data: why are we looking at this?

High-frequency financial data is certainly a `big data' problem, with all of the associated issues: what are the stylized facts of the data? What are we trying to do with the data? What are appropriate models? Industry approaches get the first two of these questions, but do badly on the third. Most academic studies do badly on all three. For example, it is a fairy tale that we can propose a time-invariant model for the evolution of high-frequency data, estimate the parameters of this model, and then apply the conclusions of an analysis that assumes that the parameters were known with certainty. In this talk, I will try to identify what we might want to do with high-frequency data, critique some existing research agendas, and illustrate a possible way of trading in a high-frequency market.

Speaker: Umberto Cherubini, Università de Bologna

Time: 18:00-19:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

No-Arbitrage Choquet Pricing with an Application to the Irrational Exercise Problem

Based on joint work with Sabrina Mulinacci.

Date: Thursday 1 December 2016

Speaker: Michael Tehranchi, University of Cambridge

Time: 17:00-18:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

Black-Scholes inequalities: applications and generalisations

Various inequalities satisfied by the Black--Scholes call pricing formula

and their applications to uniform bounds on implied volatility will be

presented. To understand from where these inequalities arise, the family of

call pricing functions is shown to be a noncommutative semigroup with

involution with respect to a certain multiplication operator which is

compatible with the convex order. A one-parameter sub-semigroup can be

identified with a peacock, providing tractable call surface parametrisation

in the spirit of the Gatheral-Jacquier SVI surface.

Speaker: Giorgia Callegaro, Università degli studi di Padova

Time: 18:00-19:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

Optimal investment in markets with over and under-reaction to information

In this paper we introduce a jump-diffusion model of shot-noise type for stock prices, taking into account over and under-reaction of the market to incoming news. We work in a partial information setting, by supposing that standard investors do not have access to the market direction, the drift, (modeled via a random variable) after a jump. We focus on the expected (logarithmic) utility maximization problem by providing the optimal investment strategy in explicit form, both under full (i.e., from the insider point of view, aware of the right kind of market reaction at any time) and under partial information (i.e., from the standard investor viewpoint, who needs to infer the kind of market reaction from data). We test our results on market data relative to Enron and Ahold. The three main contributions of this paper are: the introduction of a new market model dealing with over and under-reaction to news, the explicit computation of the optimal filter dynamics using an original approach combining enlargement of filtrations with Innovation Theory and the application of the optimal portfolio allocation rule to market data.

Date: Thursday 15 December 2016

Speaker: Suleyman Basak, London Business School and CEPR

Time: 17:00-18:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

TBA

TBA

Speaker: Anes Dallagi, EDF France

Time: 18:00-19:00

Place: University College London -Physics Building A1/3, Gower Place, London, United Kingdom

TBA

TBA

## 2015-16 London Mathematical Finance Seminar Series

The January-March 2016 programme is hosted by the King's College London (KCL)

The seminar is partially supported by INTECH

To subscribe the seminar email list: https://mailman.ic.ac.uk/mailman/listinfo/mathfin-seminar

Date: Thursday 21 January 2016

Speaker #1: Luciano Campi,  LSE

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

On the support of extremal martingale measures with given marginals

After discussing some characterisations of extremal measures with given marginals available in the literature, going from functional analysis to combinatorics, we will turn to their martingale counter-parts whose study is related to robust pricing and hedging. In particular, we will give some sufficient and necessary conditions with a geometric and combinatorial flavour for a given set to be the support of an extremal martingale measure with pre-specified discrete marginals. Some open problems will be discussed as well. This is based on joint work with Claude Martini.

Speaker #2: Ying Hu Université de Rennes 1

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

An ergodic BSDE approach to large time behaviour of  solution of semilinear parabolic partial differential equation

This talk is devoted to the study of the large time behaviour of  solution of some semilinear parabolic partial differential equation (with Dirichlet or Neumann boundary condition). A probabilistic method (more precisely, an approach via an ergodic backward stochastic equation) is developped to show that the solution of a parabolic semilinear PDE at large time  $T$ behaves like a linear term $\lambda T$ shifted  with a function $v$, where $(v,\lambda)$  is the solution of the ergodic PDE associated to the parabolic PDE.  The advantage of our method is that it gives an explicit rate of convergence. The result gives a perspective to give a precise estimate on the long run asymptotics for utility maximisation.

Date: Thursday 4 February 2016

Speaker #1: Jakša CvitanićCaltech

Time: 16:15-17:00

PlaceKing's College London- Nash Lecture Theatre K2.31

Dynamic Programming Approach to Principal-Agent Problems and Applications in Portfolio Management

We develop a new approach to solving a general finite horizon Principal-Agent problem from Contract Theory. We identify a family of admissible contracts for which  the optimal agent's action is explicitly characterized; then,  we show that we do not lose on generality when finding the optimal contract inside this family. Our argument relies on the Backward Stochastic Differential Equations approach to  non-Markovian stochastic control, and more specifically, on the most recent extensions to the second order case. As a special case example, we  apply the method to the problem of optimal compensation of a portfolio  manager.
Joint with N. Touzi and D. Possamai

Speaker #2: Miklós Rásonyi, MTA Alfréd Rényi Institute of Mathematics

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Sticky processes with jumps

We prove that sticky processes can be approximated arbitrarily well in L_p norm by processes that are martingales under an equivalent change of measure. The precise formulation of this result raises several issues which we will discuss. We also present some applications to the theory of illiquid markets.

Date: Thursday 18 February 2016

Speaker #1: Fabio Bellini, Università degli Studi di Milano-Bicocca

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Fabio Bellini here

Elicitability, expectiles and backtesting with loss functions

We review the notion of elicitable statistical functional and discuss the characterisation of expectiles as the only elicitable coherent risk measures. We investigate the financial interpretation of expectiles and their possible use as risk measures for capital requirements, in comparison with the more established Value at Risk and Expected Shortfall. Finally, we discuss how consistent loss functions, whose existence is guaranteed by the elicitability property, may be used for testing and assessing the accuracy of a risk forecasting model.

Speaker #2: Jan Obloj, University of Oxford

Time: 17:15-18:00

PlaceKing's College London- Nash Lecture Theatre K2.31

Find out more about Jan Obloj here

Robust pricing-hedging duality with path constraints and applications to information  quantification

We consider robust (pathwise) approach to pricing and hedging. Motivated by the notion of prediction set in Mykland (2003), 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. The framework interpolates between model--independent and model--specific settings. We establish a general pricing--hedging duality. The setup is parsimonious and includes the case of no traded options as well as the so-called martingale optimal transport duality of Dolinsky and Soner (2013) which we extend to multiple dimensions and multiple maturities. In presence of non-trivial beliefs, the equality is obtained between limiting values of perturbed problems indicating that the duality holds only if the market is stable under small perturbations of the inputs. Our framework allows to quantify the impact of making assumptions or gaining information. We focus in particular on the latter and study if the pricing-hedging duality is preserved under additional information.
Joint work with Zhaoxu Hou and Anna Aksamit.

Date: Thursday 3 March 2016

Speaker #1: Marco Fritelli, Università degli Studi di Milano

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Marco Fritelli here

A Unified Approach to Systemic Risk Measures via Acceptance Sets

The purpose of this paper is to specify a general methodological framework that is flexible enough to cover a wide range of possibilities to design systemic risk measures via multi-dimensional acceptance sets and aggregation functions, and to study corresponding examples. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash  that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario-dependent allocation). We illustrate with several examples the advantages of this feature. We also provide conditions which ensure monotonicity, convexity, or quasi-convexity of our systemic risk measures.

Speaker #2: Matthias Scherer, Technische Universität München (TUM)

Time: 17:15-18:00

PlaceKing's College London- Nash Lecture Theatre K2.31

Find out more about Matthias Scherer here

Exogenous shock models in high dimensions and a primer on model robustness

We review recent results on exogenous shock models and show how interesting subfamilies can be constructed in high dimensions. This is needed for applications in portfolio-credit risk and insurance. From a mathematical perspective, it bridges concepts from stochastic processes, self-similar distributions, and multivariate probability laws. Another-less obvious- application of the theory is the problem of model robustness in market risk management, for which we propose a new philosophy based on a distortion of the stochastic root of a risk model. The talk is based on joint work with Jan-Frederik Mai and Steffen Schenk.

Date: Thursday 17 March 2016

Speaker #1: Josef Teichmann, ETH Zürich

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Josef Teichmann here

Rough Term structures

In the realm of Martin Hairer's regularity structures we introduce a Sobolev type norm on spaces of modelled distributions to enable the proper use of methods from stochastic analysis. We show several examples from term structure theory where regularity structures might be of importance in mathematical Finance.
(joint work with David Proemel, ETH)

Speaker #2: Philipp Keller, Deloitte

Time: 17:15-18:00

PlaceKing's College London- Nash Lecture Theatre K2.31

Find out more about Philipp Keller here

The foundations of the valuation of insurance liabilities

Valuation of liabilities is at the core of insurers’ risk management and determines the type of products that are being sold by insurers and their investment strategies. Accounting and regulatory valuation frameworks impact the entire financial market and society. Often insurers cover policyholders from a wide variety of risks over many decades, which makes the valuation of these covers highly complex and challenging.

We discuss the purposes of different valuation frameworks that are being used by insurance companies and put the different types of valuation standards into the context of replication with financial instruments to show their differences and commonalities. We focus on economic, market consistent valuation which is based on the cost of producing insurance liabilities with traded financial instruments and on consistency requirements between best estimates, the cost of capital and discount rates.

Finally, we give an overview over the connection between valuation, systemic risk and macroprudential policies and regulations of central banks.

Date: Thursday 31 March 2016

Speaker #1: Aleksandar Mijatovic, King's College London

Time: 16:15-17:00

PlaceKing's College London- Nash Lecture Theatre K2.31

Find out more about the speaker here

A weak multilevel Monte Carlo scheme for multidimensional L\'evy-type processes

Abstract: In this talk we describe a novel weak multilevel approximation scheme for time-changed L\'evy processes and L\'evy driven SDEs. The scheme is based on the state space discretisation of the driving L\'evy process and is particularly well suited if the multidimensional driver is given by a L\'evy copula.The multilevel version of the scheme is genuinely weak as it does not require strong convergence to control the level variances. The analysis of the level variances rests upon a new coupling between the approximating Markov chains of the consecutive levels, which is defined via a coupling of the corresponding Poisson Point Processes and is easy to simulate.
This is joint work with D. Belomestny.

Speaker #2: Martino Grasselli, Finance Lab at the Pôle Universitaire Léonard de Vinci / Università Degli Studi di Padova

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Martino Grasselli here

Lie Symmetry Methods for Local Volatility Models

We investigate PDEs which are associated with the calculation of expectations for a large class of Local Volatility Models. We find nontrivial symmetry groups that can be used to obtain standard integral transforms of fundamental solutions of the PDE. We detail explicit computations in the separable volatility case when σ(t, x) = h(t)(α + βx + γx2), corresponding to the so called Quadratic Normal Volatility Model. We also consider choices for which exact fundamental solutions can be obtained.

Date: Thursday 23 June 2016

## Speaker #1: Lan WU, Peking University

Time: 16:00-17:00

PlaceKing's College London- Strand Building, S4.23

Find out more about the speaker here

Occupation Times of General Lévy Processes

Abstract: For a general Lévy process X which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of X and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of X. It is believed that our results would play an important role in ﬁnancial applications.