## 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.

The October-December 2015 programme is hosted by the Financial Mathematics and Risk and Stochastics groups at the London School of Economics and Political Science (LSE)

The seminar is partially supported by INTECH

These seminars will be held in the Thai Theatre, New Academic Building, at LSE. Maps and Directions.
All are welcome to attend. If you are attending from out the LSE, please email Ian Marshall (i.marshall@lse.ac.uk) to guarantee smooth access into the New Academic Building at the reception and security desk.

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

Date: Thursday 1 October 2015

Speaker #1: Markus Reiss, Humboldt University (!!! note the change of time and venue !!!)

Time: 16:00-17:00
Place: KCL - Strand Building, Room S0.13, Ground Floor
KCL Maps and Directions

Improved volatility estimation under one-sided errors with applications to limit order books

Abstract: For a semi-martingale X, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation <X,X> is constructed. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive n^{−1/3} as optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with n observations (in mean). This considerably improves upon the classical n^{−1/4}-rate obtained for observations under centered noise. As an application estimating the integrated volatility of an efficient price process X from intra-day order book quotes is discussed.

Joint work with Markus Bibinger and Moritz Jirak

Speaker #2: Paolo Guasoni, Dublin City University (!!! note the change of time !!!)

Time: 17:30-18:30
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Who should sell stocks?

Abstract: Never selling stocks is optimal for investors with a long horizon and a realistic range of preference and market parameters, if relative risk
aversion, investment opportunities, proportional transaction costs, and dividend yields are constant. Such investors should buy stocks when their portfolio weight is too low, and otherwise hold them, letting dividends rebalance to cash over time rather than selling. With capital gain taxes, this policy outperforms both static buy-and-hold and dynamic rebalancing strategies that account for transaction costs. Selling stocks becomes optimal if either their target weight is low, or intermediate consumption is substantial.

(Joint work with Johannes Muhle-Karbe and Ren Liu)

Date: Thursday 15 October 2015

Speaker #1: University of Toulouse 1 Capitole

Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Optimal exit under moral hazard

Abstract: We develop a model of optimal exit when a firm's asset owned by a risk-neutral principal is contracted out to a risk-neutral agent to manage. We characterize the optimal contract implementing effort at any time and prove that for a very profitable firm, it is optimal to let the agent shirk.

Keywords: Dynamic Principal-agent model, Optimal Stopping, Free boundary.

Speaker #2: Halil Mete Soner, ETH Zürich

Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Stochastic target problems

Abstract: In a stochastic target problem, the controller tries to steer the state process into a prescribed target set with certainty. The state is assumed to follow stochastic dynamics while the target is deterministic and this miss-match renders the problem difficult. One exploits the degeneracies and/or the correlations of the noise process to determine the initial positions from which this goal is feasible. These problems appear naturally in several applications in quantitative finance providing robust hedging strategies. As a convenient solution technique, we use the geometric dynamic programming principle that we will describe in this talk. Then, this characterization of the reachability sets will be discussed in several examples.

Date: Thursday 29 October 2015

Speaker #1: Pierre Cardaliaguet, Université Paris-Dauphine

Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Learning in mean-field games

Abstract: Mean field game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. The aim of this talk is to explain how such an equilibrium can appear: we introduce a learning procedure (similar to the fictitious play) and show its convergence when the mean field game is potential.

This is a joint work with S Hadikhanloo (Paris-Dauphine)

Speaker #2: Albina Danilova, LSE

Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Markov bridges: SDE representation

Abstract: Please view the attachment here (PDF attachment).

Date: Thursday 12 November 2015

Speaker #1: Philipp Harms, ETH Zürich

Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Affine representations of fractional processes with applications in mathematical finance

Abstract: Fractional processes have gained popularity in financial modelling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we show that a certain class of fractional processes can be represented as linear functionals of an infinite dimensional affine process. We demonstrate by means of several examples that the affine structure allows one to construct tractable financial models with fractional features.

Speaker #2: Marco Maggis, University of Milan

Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Arbitrage theory without a reference probability: challenges of the model-free approach

Abstract: In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: is S reduces to a singleton, absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for S being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a Universal Aggregator of all arbitrage opportunities. Furthermore we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.

The talk will be based on two papers joint with M Burzoni and M Frittelli.

Date: Thursday 26 November 2015

Speaker #1: Denis Belomestny, Duisburg Essen University

Time: 17:00-18:00
Place:
LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Higher order variance reduction for discretised diffusions via regression

Abstract: In this talk we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows one to reduce the variance up to a certain power of discretisation error. In this way the complexity order of the plain MC algorithm can be reduced down to epsilon^{-2+delta} for any delta in [0,0.5) with epsilon being the precision to be achieved. These theoretical results are illustrated by several numerical examples.

Speaker #2: Ulrich Horst, Humboldt University

Time: 18:15-19:15
Place:
LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Conditional analysis and a principal agent problem

Abstract: We analyse conditional optimization problems arising in discrete-time dynamic Principal-Agent models of delegated portfolio management. In these models, an investor (the Principal) outsources her portfolio selection to a manager (the Agent) whose investment decisions the investor cannot or does not want to monitor. We prove that if both parties' preferences are time-consistent and translation invariant and under suitable assumptions on the class of admissible contracts the problem of dynamic contract design can be reduced to a series of one-period conditional optimization problems of risk-sharing type under constraints, that the first-best solution is implementable if it exists and that optimal contracts must generally make use of derivatives. We fully solve the dynamic contracting problem for a class of optimized certainty equivalent (OCE) utilities including expected exponential utilities and Average Value at Risk. If information is generated by finitely many random walks, then our conditional optimization problems reduce to standard optimization problems in Euclidean spaces. In this case derivatives are not part of optimal compensation schemes and the contracting problem can be solved for all OCE utilities.

The talk is based on joint work with Julio Backhoff.

Date: Thursday 10 December 2015

Speaker #1: Peter Bank, TU Berlin

Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Direction

Optimal investment with price impact

Abstract: We consider a financial model with price impact where a large investor’s orders affect bid and ask prices. In a Brownian setting with exponential utility, this model allows for an explicit description of optimal investment strategies. In order to learn about indifference pricing and hedging of financial derivatives in such a frictional model, we consider a quadratic benchmark problem which emerges heuristically as the high-resilience limit of the original model. The benchmark problem also allows for a closed-form solution for very completely general options. It turns out that, rather than trading towards the currently optimal position from a frictionless reference model, it is optimal to trade towards a properly weighted average of this positions future expected values. This is joint work in progress with Mete Soner and Moritz Voss.

Speaker #2: Peter Tankov, Université Paris-Diderot (Paris 7)

Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
LSE Maps and Directions

Asymptotic lower bounds for optimal trading

Abstract: We consider the problem of tracking a target whose dynamics is modelled by a continuous Itô semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. We provide a comprehensive list of examples with explicit expressions for the lower bounds and discuss the application of our results to the problem of optimal trading in the presence of transaction costs.