The Risk and Stochastics Seminar aims to promote communication and discussion of research in the mathematics of insurance and finance and their interface, to encourage interaction between practice and theory in these areas, and to support academically students in related programmes at postgraduate level. All are welcome to attend. Sessions run regularly during LSE terms, and will place on Thursdays at 6.05 pm in Room V312, 3rd floor of Tower 2.

The current up-to-date schedule is given below. Please contact Events for further information about any of these seminars. All are very welcome to attend.

20 September 2012	Elisa Alos (Universistat Pompeu Fabra) 17:00 - 18:00, COL 6.15 Leverhulme Library, Department of Statistics, Columbia House (6th Floor) Title: A decomposition formula for option prices in the Heston model and applications to option pricing approximation' Abstract: By means of classical Itôs calculus we decompose option prices as the sum of the classical Black-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due to correlation and a term due to the volatility of the volatility. This decomposition allows us to develop first and second-order approximation formulas for option prices and implied volatilities in the Heston volatility framework, as well as to study their accuracy for short maturities. Numerical examples are given.
10 May 2012	Brenda Lopez Cabrera (Humboldt-Universität zu Berlin) 17.00, Rm OLD 3.28 Details can be found here.
3 May 2012	Larbi Alili (University of Warwick) - 17.00-18.00 in CON 1.04 Title: On some involutive inversions of one dimensional diffusions Abstract: Given a regular one dimensional diffusion on an interval, where regular boundaries are killing, we show that, in some sense, this has a unique inverse with respect to a fixed point in the state space. This inverse process when appropriately time-changed is the dual process which law is obtained by Doob $h$-transforming the law of the original diffusion. Conversely, given a positive harmonic function $h$ on that interval (or a scale function) , satisfying some reasonable conditions, we show that the Doob $h$-transformed process can be obtained explicitly in terms of inversion of the original diffusion with a time change. The construction involves some involutions and interesting random clocks. This is joint work with P. Graczyk and T. Zak.
19 April 2012	Luciano Campi (Paris 13) - 17.00-18.00 in V312 Title: On existence of shadow prices Abstract: For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless shadow market that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample that shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid-ask-spreads. This talk is based on a joint work with G. Benedetti, J. Kallsen and J. Muhle-Karbe.
29 March 2012	Samuel Cohen (Oxford University) Title: Uncertainty and nonlinear expectations Abstract: Decision making in the presence of uncertainty is a mathematically delicate topic. In this talk, we consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering discrete-time `martingale' processes, we show that the classical results of martingale convergence and the up/downcrossing inqualities hold in a `quasi-sure' sense. We also give conditions, for a general filtration, under which an `aggregation' property holds, generalising an approach of Soner, Touzi and Zhang (2011). From this, we extend various results on the representation of conditional sublinear expectations to general filtrations under uncertainty.
15 March 2012	Josef Teichmann (ETH Zurich) Details can be found here.
8 March 2012	Johan Tysk (Uppsala University) Title: Can time-homogeneous diffusions produce any distribution? Abstract: Given a centred distribution, can one find a time-homogeneous martingale diffusion starting at zero which has the given law at time 1? We answer the question affirmatively if generalized diffusions are allowed. This talk is based on a joint work with Erik Ekström, David Hobson and Svante Janson.
1 March 2012	Suleyman Basak (London Business School) Title: Strategic Asset Allocation in Money Management Abstract: Money managers behave strategically when competing for fund flows within relatively small groups. We study strategic interaction between two risk-averse managers in continuous time, characterizing analytically their unique equilibrium dynamic investments. Driven by chasing and contrarian mechanisms when one is well ahead, they gamble in the opposite direction when their performances are close. We also discuss multiple and mixed-strategy equilibria. Equilibrium policy of each crucially depends on the opponent's risk attitude. Hence, client investors, concerned about how a strategic manager may trade on their behalf, should also learn competitors' characteristics -- as against non-strategic settings, where knowing a manager's own characteristics suffices to determine behavior.
23 February 2012	Vicky Henderson (Oxford MAN Institute) Details can be found here.
16 February 2012	Mike Tehranchi (University of Cambridge) Details can be found here.
13 Feb 2012 Start time 4pm Venue: Room COL 6.15, sixth floor, Columbia House.	Albert Shiryaev (Steklov Mathematical Institute) Title: The concept of randomness: evolution of noyions Abstract: We analyze different notions of randomness for infinite sequences and their relations starting with the notion of "Kollective" on von Mises. His definition of "randomness" provoked serious criticisms, however it also stimulated the investigation of the problem "which infinite sequences meet our idea of randomness?" We give an overview of different algorithmic approaches, including: Frequency-stability randomness after Mises-Wald-Church Frequency-stability randomness after Kolmogorov Typical randomness after Martin-Loef Chaotic randomness or Complex structure after Kolmorgorov-Levin-Schnorr We shall also discuss the relation between these algorithmic approaches and the probabilistic ones. Albert Shiryaev is a distinguished Visiting Professor in the Deaprtment of Statistics.
9 February 2012	Markus Riedle (King's College) Title: Stochastic models in infinite dimensions Abstract: Starting from the Heath-Jarrow-Morton framework and the heat equation we motivate examples of noise for models in an infinite dimensional setting such as Wiener processes, Levy processes and fractional Brownian motions.In more detail we consider the recently introduced cylindrical Levy process as a generalisation of cylindrical Wiener processes, which are the most often applied model of noise in infinite dimensions.The perturbation of dynamics by noise results in stochastic differential equations and requires a theory of stochastic integration in the underlying space which is in this setting infinite dimensional. We explain the difficulties of stochastic integration in infinite dimensional spaces and indicate a possible approach. (part of this talk is based on joint works with D. Applebaum, O. van Gaans, E. Issoglio)
2 February 2012	Curdin Ott (University of Bath) Title: Capped Optimal Stopping problems for the Maximum Process Abstract: This talk concerns optimal stopping problems driven by a spectrally negative Levy process X. More precisely, we will consider capped versions of the Russian and American lookback optimal stopping problem and provide semi-explicit solutions in terms of scale functions. The optimal stopping boundary is characterised by an ordinary first-order differential equation involving scale functions and, in particular, changes according to the path variation of X. Furthermore, we will see that the solutions exhibit a pattern suggested by Peskir's maximality principle.
19 January 2012	Damiano Brigo (King's College) Details can be found here.
12 January 2012	Johannes Ruf (Oxford University) Details can be found here.
8 December 2011	Alex Mijatovic (University of Warwick) Title: On the drawdown of completely asymmetric Levy processes This is joint work with M. Pistorius.
24 November 2011	Kees van Schaik (University of Manchester) Title: Meromorphic Levy processes: a Wiener-Hopf Monte Carlo simulation method and American option pricing Abstract: Recently some new, large families of Levy processes (processes with stationary independent increments and cadlag paths) have been introduced that have the rare property that both the parameters determining their law and their Wiener-Hopf factors are quite explicitly known. The latter firsly allows for using such processes in a newly established so-called Wiener-Hopf Monte Carlo (WHMC) simulation method. We will discuss this simulation method and point out some advantages over 'plain' Monte Carlo, we will also discuss some work in progress concerning extending the WHMC simulation method to path functionals such as first hitting times and over/undershoots. Secondly we will discuss some work in progress concerning a numerical scheme for finite expiry optimal stopping problems (i.e. finite horizon American options in a financial context) driven by such Levy processes, extending Peter Carr's so-called Canadisation algorithm
17 November 2011	Mete Soner (ETH Zürich) Title: Choquet Capacity, Nonlinear PDE's and hedging Abstract: As it is well known backward stochastic differential equations (BSDE's) are naturally connected to semilinear parabolic partial differential equations. Moreover there are many applications of BSDE's in mathematical finance. The semilinear part of the equation, determines the quadratic variation and allows us to work with one probability measure. To obtain a similar theory for fully nonlinear parabolic equations, one needs to extend the theory and require the equations to hold under a large class non-dominated measures. In this talk, I will survey this new theory of 2BSDE's, G- expectations of Peng, uncertain volatility model as developed by Denis & Martini. I will also provide a hedging or equivalently a martingale representation theorem in this context.
10 November 2011	Kevin Warner (Tower Research Capital) Title: Neural Networks for Systematic Trading Abstract: Starting with a background on artificial neural networks, an intuitive explanation of the basic perceptron and a review of the process for estimation, training and evaluation, focusing on where nuance is particularly needed, I'll then cover the thinking behind various architectures and topologies and will compare the computing overhead and forecasting accuracy of assorted models by working though examples on simulated and actual time series data, concluding with some recommendations for real life implementation.
3 November 2011	Jordan Stoyanov (University of Newcastle) Details can be found here.
27 October 2011	Huyên Pham (University Paris Diderot) Details can be found here.
20 October 2011	Ragnar Norberg (LSE and University of Lyon) Title: On optimal quadratic hedging of payment streams and optimal design of derivatives Abstract: An investment strategy consists of a portfolio process and a cost process, the latter representing deposits into and withdrawals from the portfolio account. The investment strategy is a hedge of a contractual payment stream (e.g. defined by an insurance contract) if the payments are currently deposited on or withdrawn from the portfolio account as they are due. The purpose of the hedge is given by an optimization criterion for the investment strategy. In the martingale case certain quadractic criteria lead to the same optimal portfolio but different optimal cost functions. The theory works when constraints are imposed on the portfolio value, a case in point being solvency requirements in insurance (e.g. Solvency II). So far the theory has dealt with optimal hedging with a given set of available traded assets. I shall finish by discussing optimal design of the very assets (e.g. insrance derivatives), the purpose being to minimise the average hedging error across a population of hedgers pursuing optimal individual hedging strategies.
13 October 2011	Almut Veraart (Imperial College London) Details can be found here.
6 Oct 2011	Roman Muraviev (ETH) Title: Natural selection with habits and learning in heterogenous economics Abstract: We study natural selection in complete financuial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and learning mechanism, risk aversion, impatience (time preference rate) and degree of habits. We develop new techniques for studying long run behaviour of such economics, based on the Strassen's functional law of iterated logatrithm. In particular, we explicitly detrmine an agent's survival index and show how the latter depends on the aent's characteristics. We use these results to study the long run behaviour of the equilibrium interest rate and the market price of risk.

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