### The 2014-15 London Mathematical Finance Seminar Series will be hosted by University College London in the second term of the academic session.

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

The seminar is partially supported by INTECH.

**Date: 15 January 2015**

**Speaker: **Andrew Papanicolaou**, University of Sydney**

Time: 16:30-17:30

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions**

Abstract: We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions. We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns.The results are an extension of the partially-informed investment strategies obtained by the Black-Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.

**Speaker: **Christoph Kuehn**, ****J.W. Goethe-Universität, Frankfurt**

Time: 17:45-18:45

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Modeling capital gains taxes in continuous time**

Abstract: In most countries, trading gains have to be taxed. The modeling is complicated by the rule that gains on assets are taxed when assets are sold and not when gains actually occur. This means that an investor can influence the timing of her tax payments, i.e., she holds a timing option. In this talk, it is shown how the tax payment stream can be constructed beyond trading strategies of finite variation. We give an example for tax-efficient strategies for which the tax payment stream can be computed explicitly and show for which trading strategies the tax payment process is of (in)finite variation. Finally, we solve an optimal stopping problem that illustrates the basic effect of taxes on optimal investment decisions. This confirms the conjecture that the value of the tax-timing option is increasing in the volatility of the asset the investor holds. (The talk is based on joint work with Björn Ulbricht and partly with Budhi Arta Surya)

**Date: 29 January 2015**

**Speaker: ****Damiano Brigo,**** Imperial College London**

Time: 16:30-17:20

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Nonlinear valuation under credit gap risk, collateral margins, funding costs and multiple curves**

Abstract: Following a quick introduction to derivatives markets and the classic theory of valuation, we describe the changes triggered by post 2007 events. We re-discuss the valuation theory assumptions and introduce valuation under counterparty credit risk, collateral posting, initial and variation margins, and funding costs. A number of these aspects had been investigated well before 2007. We explain model dependence induced by credit effects, hybrid features, contagion, payout uncertainty, and nonlinear effects due to replacement closeout at default and possibly asymmetric borrowing and lending rates in the margin interest and in the funding strategy for the hedge of the relevant portfolio. Nonlinearity manifests itself in the valuation equations taking the form of semi-linear PDEs or Backward SDEs. We discuss existence and uniqueness of solutions for these equations. We present an invariance theorem showing that the final valuation equations do not depend on unobservable risk free rates, that become purely instrumental variables. Valuation is thus based only on real market rates and processes. We also present a high level analysis of the consequences of nonlinearities, both from the point of view of methodology and from an operational angle, including deal/entity/aggregation dependent valuation probability measures and the role of banks treasuries. Finally, we hint at how one may connect these developments to interest rate theory under multiple discount curves, thus building a consistent valuation framework encompassing most post-2007 effects.

**Speaker: **Claude Martini**, Zeliade Systems**

Time: 17:45-18:35

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Investigating the extremal martingale measures with pre-specified marginals**

Abstract: The extremal points in the set of all measures with pre-specified marginals, without the martingale constraint, have been extensively studied by many authors in the past (e.g. Denny, Douglas, Letac, Klopotowski to cite only a few). In this talk, we will focus on the characterization provided by Denny in the countable case: a key property is that the support of the probability Q has no “cycle”, otherwise a perturbation of Q can be constructed so that Q can not be extremal. In the context of the 2 marginals martingale problem studied by Beiglböck-Juillet, with special cases provided by Henry-Labordère and Touzi, Hobson and Klimmeck, Hobson and Neuberger, and Laachir, we give examples of extremal and non-extremal points, and give partial results towards a characterization theorem. (Joint work with L. Campi, LSE)

**Date: 12 February 2015**

**Speaker: **Julien Hugonnier**, EPFL**

Time: 16:30-17:20

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Heterogeneity in Decentralized Asset Markets**

Abstract: We study a search and bargaining model of an asset market, where investors’ heterogeneous valuations for the asset are drawn from an arbitrary distribution. Our solution technique renders the analysis fully tractable and allows us to provide a full characterization of the equilibrium, in closed form, both in and out of steady state. We use this characterization for two purposes. First, we establish that the model can naturally account for a number of stylized facts that have been documented in empirical studies of over-the-counter asset markets. In particular, we show that heterogeneity among market participants implies that assets are reallocated through “intermediation chains,” ultimately producing a core-periphery trading network and non-trivial distributions of prices and trading times. Second, we show that the model generates a number of novel results that underscore the importance of heterogeneity in decentralized markets. We highlight two: first, heterogeneity magnifies the price impact of search frictions; and second, search frictions have larger effects on price levels than on price dispersion. Hence, quantifying the price discount or premium created by search frictions based on observed price dispersion can be misleading.

**Speaker: **Matthieu Rosenbaum**, ****Université Pierre et Marie Curie**

Time: 17:45-18:35

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Volatility is rough **

Abstract: Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H<1/2. We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not long memory in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact. Finally, we provide a quantitative market microstructure-based foundation for our findings, relating the roughness of volatility to high frequency trading and order splitting. This is joint work with Jim Gatheral and Thibault Jaisson.

**Date: 26 February 2015**

**Speaker: ****Stefan Ankirchner,**** Universität Jena**

Time: 16:30-17:20

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title*: ***A generalized Donsker theorem and approximating SDEs with irregular coefficients**

Abstract: We provide a new method for approximating the law of a diffusion M solving a stochastic differential equation with coefficients satisfying the Engelbert-Schmidt conditions. To this end we construct Markov chains whose law can be embedded into the diffusion M with a sequence of stopping times that have expectation 1/N, where N is a discretization parameter.

The transition probabilities of the Markov chains are determined by a reference probability measure, scaled with a factor depending on N and the state. We show that the Markov chains converge in distribution to the diffusion M, thus refining the Donsker-Prokhorov invariance principle. For some cases we provide a convergence rate. Finally, we illustrate our results with several examples. The talk is based on joint work with Thomas Kruse and Mikhail Uruso

**Speaker: **Bruno Bouchard**,**** ****Université Paris-Dauphine**

Time: 17:45-18:35

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Almost-sure hedging with permanent price impact**

**Date: 12 March 2015**

**Speaker: **Ulrich Horst, **Humboldt-Universität, Berlin**

Time: This talk has been cancelled.

Title: **Weak law of large numbers for a limit order book model with fully state dependet order dynamics**

Abstract: We study a one-sided limit order book (LOB) model, in which the order dynamics depend on both, the current best bid price and the current volume density function. For the joint dynamics of the best bid price and the standing buy volume density we derive a weak law of large numbers, which states that the LOB model converges to a continuous-time limit when the size of an individual order as well as the tick size tend to zero and the order arrival rate tends to infinity. In the scaling limit the standing buy volume density follows a non-linear PDE coupled with a non-linear ODE that describes the best bid price. The talk is based on joint work with Doerte Kreher.

**Speaker: ****Huyên Pham****,**** ****Université Paris-Diderot**

Time: 17:45-18:35

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **An optimal trading problem in intraday electricity markets**

**Date: 19 March 2015**

**Speaker:** Thaleia Zariphopoulou, **University of Texas at Austin**

Time: 16:30-17:20

Place: NASH LECTURE THEATRE (K2.31), Strand Campus, KING'S COLLEGE

Title: Forward investment performance processes: review and open problems

Abstract:In this talk, I will discuss the concept of forward investment performance process and will present results on discrete and continuous time. The latter are related to a fully-non linear SPDE, and to ergodic and infinite horizon BSDE. I will also state some open problems in asset allocation under these alternative criteria.

**Date: 26 March 2015**

**Speaker: **Tomasz Bielecki, **Illinois Institute of Technology**

Time: This talk has been cancelled.

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Market making via sub-scale invariant Dynamic Acceptability Indices**

Abstract: The main goal of this study is to develop a general theoretical pricing framework that will capture some practically relevant properties, such as: the prices are not homogeneous in number of shares traded; the underlying securities bear transaction costs; the securities pay dividends; the dividends may be different for a long or short position. To achieve this goal, we use sub-scale invariant Dynamic Acceptability Indices (DAIs) as the main tool in developing thepricing methodology, and consequently, we present a representation of proposed prices in terms of a class of Backward Stochastic Difference Equations and g-Expectations. Besides the above mentioned properties, we also prove that: considered market models do not admit arbitrage; bid and ask prices do shrink the super hedging pricing interval; the prices are time consistent in some appropriate sense; if the drivers are linear we recover the classical martingale pricing theory. Finally, we provide some practical examples.

**Speaker: **Ernst Eberlein**,**** University of Freiburg**

Time: 17:45-18:35

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: **Lévy driven two price valuation with applications to long-dated contracts**

**Date: 21 May 2015****Reducing model risk via additional (in)dependence assumptions**

**Date: 18 June 2015****Separating Skilled and Unskilled Fund Managers by Contract Design**

**Advancing the universality of numerical integration methods to any underlying process for option pricing**

Exceptional accuracy and speed for option pricing are available via quadrature (Andricopoulos et al., JFE, 2003), extending into multiple dimensions with complex path-dependency and early exercise (Andricopoulos et al., JFE, 2007). However, the technique was incomplete, leaving many modelling processes outside the Black-Scholes-Merton framework unattainable. In this seminar paper (following Chen, Harkonen and Newton, JFE, 2014), I discuss how to remove the remaining major block to universal application. Although this had appeared highly problematic, the solution turns out to be conceptually simple and implementation is straightforward. Crucially, the method retains its speed and flexibility across complex combinations of option features but is now applicable across other underlying processes.