### 2016-17 London
Mathematical Finance Seminar Series

### The October-December programme will be hosted by University College
London (UCL).

The seminar is partially supported by INTECH.

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

Find out more about Lukasz Szpruch here

**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

Find out more information about Mikko Pakkanen here

**Modelling and forecasting rough volatility**

__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

Find out more about Christoph Reisinger here

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

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

Find out more about Ales Cerny here

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

Speaker: **Antoine Jacquier**, Imperial College London

Time: 17:00-18:00

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

Find out more about Antoine Jacquier here

**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

Find out more about Chris Rogers here

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

Speaker: **Umberto Cherubini**, Università de Bologna

Time: 18:00-19:00

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

Find out more about Umberto Cherubini here

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

__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

Find out more about Michael Tehranchi here

**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

Find out more about Giorgia Callegaro here

**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

Find out more about Suleyman Basak here

**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**

## 2015-16 London Mathematical Finance Seminar Series

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

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

Find out more information of Luciano Campi here

**On the support of extremal martingale measures with given marginals**

Speaker #2: **Ying Hu**** **Université de Rennes 1

Time: 17:15-18:00

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

Find out more information of Ying Hu here

**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 Cvitanić**, Caltech

Time: 16:15-17:00

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

Find out more information about Jakša Cvitanić here

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

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

Find out more information about Miklós Rásonyi here

**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

Place: King'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**

**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

Place: King'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

Place: King'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

Place: King'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**

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

Place: King's College London- Strand Building, S4.23

Find out more about the speaker here

**Occupation Times of General Lévy Processes**