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

Date: Thursday 30 November 2017

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

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

Date: Thursday 14 December 2017

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


Speaker #2:Elise Gourier
Time: 16:15-17:00
Place: King's College London, Room K3.11



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