2017-2018 Seminars

2017-18 London Mathematical Finance Seminar Series

The October-December 2017 programme is hosted by King's College London.

Date: Thursday 5 October 2017

Speaker #1: Martin Haugh, Imperial College
Time: 16:15-17:00
Place: King's College London, Room K3.11

Title: Markov Decision Processes and Information Relaxations

High-dimensional Markov decision processes (MDPs) are ubiquitous in fields ranging from finance and economics to engineering and operations research. These problems are generally intractable due to the so-called "curse of dimensionality" and so we must make do with sub-optimal policies in practice. But how should we evaluate the quality of these policies? In recent years duality methods based on information relaxations have been developed to answer this question. These methods proceed by using the sub-optimal policy to construct lower and upper bounds on the unknown (and impossible to compute) optimal value function. Moreover a strong duality result implies that better sub-optimal policies should yield tighter bounds, thereby producing a ``certificate'' of near-optimality for policies that are close to optimal.

In this talk we discuss some recent developments and applications of this information relaxation approach. These applications include inventory control, multi-class queuing control and tax-aware dynamic portfolio optimization. On the methodological side, we discuss extensions to infinite horizon problems and the development of change-of-measure arguments to facilitate the solution of the dual control problems. We show that similar change-of-measure arguments can be used to extend the approach to partially observed Markov decision processes (POMDPs), an important extension that we will demonstrate with an application from robotic control.

The talk will be based on results from the following papers as well as ongoing research.

[1] Tax-Aware Dynamic Asset Allocation (2016), with Garud Iyengar and Chun Wang. Operations Research (2016). Available at http://www.columbia.edu/~mh2078/OR_TaxAssetAllocation_Published.pdf
[2] Information Relaxation Bounds for Infinite Horizon Markov Decision Processes (2015), with David Brown. Forthcoming in Operations Research. Available at http://www.columbia.edu/~mh2078/infinite_horizon_R3_final.pdf
[3] Information Relaxations Bounds for Partially Observed Markov Decision Processes (2017), with Octavio Ruiz Lacedelli. Working paper. Available at http://www.columbia.edu/~mh2078/POMDP_IR_paper.pdf

Speaker #2: Andreas Kyprianou, University of Bath
Time: 17:15-18:00
Place: King's College London, Room K3.11

Title: Sphere stepping algorithms for Dirichlet-type problems with the fractional Laplacian
 We review the sphere-stepping algorithm for simulating the solution to the classical Dirichlet problem and consider whether the same can be done when the Laplacian can be changed to the fractional Laplacian. Whereas in the former case, we need knowledge about isotropic Brownian motion, in the latter case, we need information about isotropic stable Levy processes. We will show that the stable case offers a “faster” convergence than in the Brownian case thanks to the trajectory of stable processes having jumps.

Date: Thursday 19 October 2017

Speaker #1:Martin Herdegen,Warwick University
Time: 16:15-17:00
Place: King's College London, Room K3.11

Title: Equilibrium Returns with Transaction Costs

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward-backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time. 
The talk is based on joint work with Bruno Bouchard, Masaaki Fukasawa and Johannes Muhle-Karbe.

Date: Thursday 2 November 2017

Speaker #1: Dirk Becherer, Humboldt University, Berlin, Germany
Time: 16:15-17:00
Place: King's College London, Room K3.11

Title: Good Deal Hedging and Valuation Under Combined Uncertainty About Drift and Volatility

We derive robust good-deal hedges and valuations under combined model ambiguity about the drift and volatility of asset prices for incomplete markets. Good-deal valuations are determined such that not just opportunities for arbitrage but also for overly attractive reward-to-risk ratios are excluded, by restricting instantaneous Sharpe ratios for any market extension by derivatives. From a finance point of view, this permits for hedges and valuation bounds than are less extreme (respectively expensive) than those from the more fundamental approach of almost-sure superhedging and its corresponding no-arbitrage bounds. In mathematical terms, it demands however that not just ambiguities about the volatility but also about the drift become relevant. For general measurable contingent claims, possibly path-dependent, the solutions are described by 2nd-order backward stochastic differential equations with non-convex drivers, building on recent research progress on non-linear kernels. Hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures, uniformly over all priors.

Speaker #2: Thorsten Rheinlaender,Vienna University of Technology
Time: 17:15-18:00
Place: King's College London, Room K3.11

Title: Brownian trading excursions

We study a parsimonious, but non-trivial model of the limit order book. In contrast to market orders which get executed instantaneously, limit orders are placed away from the current market price (which we will call mid-price), and get executed once the mid-price process hits the limit level. Hence the volume of orders in the limit order book constitutes a random field where the space parameter corresponds to the limit level relative to the mid-price. The volume field satisfies the stochastic heat equation with multiplicative noise. We will solve this equation in terms of a local time functional. Furthermore, we study different types of trades via excursion theory.

Date: Thursday 16 November 2017

Speaker #1Clemence Alasseur, EDF Paris
Time: 16:15-17:00
Place: King's College London, Room K3.11

Title : An adverse selection approach to power pricing

We study the optimal design of electricity contracts among a population of consumers with different needs. This question is tackled within the framework of Principal-Agent problem in presence of adverse selection. The particular features of electricity induce an unusual structure on the production cost, with no decreasing return to scale. We are nevertheless able to provide an explicit solution for the problem at hand. The optimal contracts are either linear or polynomial with respect to the consumption. Whenever the outside options offered by competitors are not uniform among the different type of consumers, we exhibit situations where the electricity provider should contract with consumers with either low or high appetite for electricity. Joint work with Ivar Ekeland, Romuald Elie, Nicolás Hernández Santibáñez, Dylan Possamaï

Speaker #2: Eyal Neuman, Imperial College
Time: 17:15-18:00
Place: King's College London, Room K3.11

Title: Optimal Portfolio Liquidation in Target Zone Models

We study optimal buying and selling strategies in target zone models.  In these models the  price  is  modeled  by  a  di usion  process  which  is  reflected  at  one  or  more  barriers.   Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank intervention.  We consider the optimal portfolio liquidation problem for an investor for whom prices are optimal at the barrier and who creates temporary price impact. This problem will be formulated as the minimization of a cost-risk functional over strategies that only trade when the price process is located at the barrier.  We solve the corresponding singular stochastic control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess.  In this setting the catalyst is a set of points which is given by the barriers of the price process. Later, we consider the case where the investors create an additional permanent impact. The  central  bank,  who  wishes  to  keep  the  currency  exchange  rate  above  a  certain  barrier, therefore  needs  to  buy  its  own  currency.   The  permeant  price  impact,  which  is  created  by the  transactions  of  both  sides,  turns  the  optimal  trading  problems  of  the  trader  and  the central  bank  into  coupled  singular  control  problems,  where  the  common  singularity  arise from  a  local  time  along  a  random  curve.   We  solve  the  central  bank's  control  problem  by means of the Skorokhod map and derive the trader's optimal strategy by solving a sequence of approximated control problems.
This is joint work with Alexander Schied.

Date: Thursday 30 November 2017

Speaker #1: David Skovmand
Time: 16:15-17:00
Place: King's College London, Room K3.11

Title : Rational Models for Inflation Linked Derivatives
We construct a model for the pricing and risk management of inflation derivatives. The model is rational in the sense that the real pricing kernel is a rational function of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that allows for closed form pricing of  vanilla inflation products such a zero coupon swaps, caps and floors, year-in-year swaps, caps and floors as well as the exotic LPI swap. Furthermore the model retains the attractive features of a nominal multicurve interest rate model such as closed form pricing of nominal swaptions. Finally we study how the model can be calibrated to EUR data.

Speaker #2: Giulia di Nunno, University Oslo, Norway 
Time: 17:15-18:00
Place: King's College London, Room K3.11

Title: Fully-dynamic risk-indifference pricing

We deal with dynamic pricing of financial products in an incomplete market and we focus on risk-indifference pricing. This can be seen as an alternative to the classical utility-indifference pricing in which the performance is written in terms of evaluation of risks instead of utility.
We propose a fully-dynamic risk-indifference criteria, in which a whole family of risk measures  is considered. This is based on the concept of fully-dynamic risk measures which extends the one of dynamic risk measures by adding the actual possibility of changing the perspective on how to measure risk over time. Our framework fits well the study of both short and long term investments. Risk-indifference pricing has been studied from the point of view of how to find a solution under different assumptions on the underlying dynamics and information flows. Typically the price is also evaluated at the time of the initial investment t=0. We are interested in studying the risk-indifference pricing criterion in its time evolution in a setting free from specific choices of underlying dynamics. In the dynamic framework we analyse whether the risk-indifference criterion actually provides a proper convex price system. Furthermore, we consider the relationship of the fully-dynamic risk-indifference price with no-good-deal bounds. Recall that no-good-deal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fully-dynamic risk measure so that the corresponding risk-indifference prices satisfy the no-good-deal bounds. As it turns out, no-good-deal bounds also provide a method to select the risk measures that provide a proper fully-dynamic risk-indifference price system.

Date: Thursday 14 December 2017

Speaker #1: Umut Cetin,London School of Economics
Time: 16:15-17:00
Place: King's College London, Room K3.11

Title: Financial equilibrium with aymmetric information and random horizon

We study in detail and explicitly solve the version of Kyle's model introduced in a specific case by Back and Baruch, where the trading horizon is given by an exponentially distributed random time. We first focus on time-homogeneous equilibria using tools from the theory of one-dimensional diusions. It turns out that such an equilibrium is only possible if the final payoff is Bernoulli distributed. We shall show later that for a payoff with general distribution the equilibrium exists and is a time-changed version of the Bernoulli case.  In both cases we characterise explicitly the equilibrium price process and the optimal strategy of the informed trader. Contrary to the original Kyle model it is found that the reciprocal of market's depth, i.e. Kyle's lambda, is a uniformly integrable supermartingale. While Kyle's lambda is a potential, i.e. converges to 0, for the Bernoulli distributed final payoff, its limit in general is different than 0.

Speaker #2: 
Alvaro Cartea,Oxford University
Time: 17:15-18:00
Place: King's College London, Room K3.11

Title: Maximizing Fill Ratios in Foreign Exchange Markets with Latency and Random Delays

We analyse how latency affects the strategies of foreign exchange (FX) traders that send liquidity taking orders to the FX electronic exchange. Latency is the time delay between a signal and a response as a result of the time it takes for the signal to travel inside the automated trading system of the Exchange and the hardware of the traders.  Latency affects the prices and fill ratios  obtained by traders -- by the time the exchange receives a trader's order, exchange rates could have moved, so trader may get a better or worse price or may not even get her order filled.   In this paper we assume that traders send marketable orders with a price limit and targets a fill ratio (FR), defined as the number of orders that are filled divided by the total number of sent orders over a period of time (e.g. a trading day).  We develop a model that maximizes FR whilst minimising how deep the marketable orders can walk the FX exchange's limit order book. We employ a proprietary data set with trader identifiers to categorise traders as: momentum or noise traders. We use traders' liquidity taking orders to show the performance of our proposed dynamic trading strategy.

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