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Seminar Series

Probability and Financial Mathematics

School of Mathematics, University of Leeds

2019/2020

Prof. Teemu PENNANEN  (King's College London)

10th of October

2:00 pm

LT 3

Roger Stevens Building

Title

Convex duality in optimal investment and contingent claim valuation in illiquid markets

Abstract

We develop a duality theory for optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions decompose into three terms, corresponding to the agent's risk preferences, trading costs and portfolio constraints, respectively. The dual representations are shown to be valid when the market model satisfies an appropriate generalization of the no-arbitrage condition and the agent's utility function satisfies an appropriate generalization of asymptotic elasticity conditions. When applied to classical liquid market models or models with bid-ask spreads, we recover well-known pricing formulas in terms of martingale measures and consistent price systems. Building on the general theory of convex stochastic optimization, we also obtain optimality conditions in terms of an extended notion of a "shadow price". The results are illustrated by establishing the existence of solutions and optimality conditions for some nonlinear market models recently proposed in the literature. Our results allow for significant extensions including nondifferentiable trading costs which arise e.g. in modern limit order markets where the marginal price curve is necessarily discontinuous.

Dr. Jing YAO  (Heriot Watt University)

24th of October

2:00 pm

LT3

Roger Stevens Building

Title

Downside Risk Optimization with Random Targets and Portfolio Amplitude

Abstract

In this paper, we rationalize using downside risk optimization subject to a random target in portfolio selection.  In context of normality, we derive analytical solutions to the downside risk optimization with respect to random targets and investigate how the random target affects  the  optimal  solutions.   In  doing  so,  we  propose  using  portfolio amplitude, as a new measure in literature, to characterize the investment strategy.  Particularly, we demonstrate the mechanism by which the  random  target  inputs  its  impact  into  the  system  and  alters  the optimal portfolio selection.  Our results underpin why investors prefer holding some specific assets in following random targets and provide explanations for some special investment strategies, such as constructing a stock portfolio following a bond index.  Numerical examples are presented to clarify our theoretical results.

Dr. Kathrin Glau  (Queen Mary University London)

7th of November

2:00pm

LT3

Roger Stevens Building

Title

Low-Rank Tensor Approximation for Parametric Option Pricing

Abstract

Computationally intensive problems in finance are characterized by their intrinsic high-dimensionality which often is paired with optimizations leading to nonlinearities. While classical numerical methods typically suffer from a curse in dimensionality, machine learning approaches promise to yield fairly accurate results with a method that is scalable in the dimensions. Computational intense training phases and the required large set of training data pose some of the major challenges for the development of new and adequate numerical methods for finance. Merging classical numerical techniques with learning methods we propose a new approach to option pricing in parametric models. The work is based on [1] and ongoing research with Paolo Colusso and Francesco Statti.

[1] Glau, K.; Kressner, D.; Statti, F.: Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing.  preprint 2019

Dr. Gonçalo dos Reis  (University of Edinburgh)

14th of November

2:00 pm

LT 3

Roger Stevens Building

Title

Itô-Wentzell for measure dependent random fields under full and conditional measure flows

Abstract

We show several Itô-Wentzell formulae on Wiener spaces for real-valued maps depending on measures. We present both the full measure-flow and the marginal-flow cases where the measure flow derivatives are understood in the sense of Lions.

 

This talk has been cancelled.

Dr. Renyuan XU  (University of Oxford)

21st of November

2:00 pm

LT3

Roger Stevens Building

Title

A Case Study on Pareto Optimality for Collaborative Stochastic Games

Abstract

Pareto Optimality (PO) is an important concept in game theory to measure global efficiency when players collaborate. In this talk, we start with the PO for a class of continuous-time stochastic games when the number of players is finite. The derivation of PO strategies is based on the formulation and analysis of an auxiliary N-dimensional central controller’s stochastic control problem, including its regularity property of the value function and the existence of the solution to the associated Skorokhod problem. This PO strategy is then compared with the set of (non-unique) NEs strategies under the notion of Price of Anarchy (PoA). The upper bond of PoA is derived explicitly in terms of model parameters. Finally, we characterize analytically the precise difference between the PO and the associated McKean-Vlasov control problem with an infinite number of players, in terms of the covariance structure between the optimally controlled dynamics of players and characteristics of the no-action region for the game. This is based on joint work with Xin Guo (UC Berkeley).

Dr.  Máté GERENCSER  (IST Austria)

22nd of November

2:00 pm

LT3

Roger Stevens Building

Title

Boundary renormalisation of stochastic PDEs
 

Abstract

We discuss solution theories of singular SPDEs endowed with various boundary conditions. In several examples  nontrivial boundary effects arise and another layer of renormalisation is required. We outline how these are connected to spatial singularities of simple trees in equations like the KPZ, PAM, of Phi^4.

Dr. Luitgard VERAART (London School of Economics)

5th of December

2pm

LT3

Roger Stevens Building

Title

When does portfolio compression reduce systemic risk?

Abstract

We analyse the consequences of portfolio compression on systemic risk. Portfolio compression is a post-trading netting mechanism that reduces gross positions while keeping net positions unchanged and it is part of the financial legislation in the US (Dodd-Frank Act) and in Europe (European Market Infrastructure Regulation).  We derive necessary structural conditions for portfolio compression to be harmful and discuss policy implications. In particular, we show that the potential danger of portfolio compression comes from defaults of firms that conduct portfolio compression. If no such defaults occur, then portfolio compression reduces systemic risk.          

 

Prof. Dr. David PRÖMEL (Mannheim Universität)

12th of December

2:00 pm

LT 3

Roger Stevens Building

Title

Martingale Optimal Transport in Robust Finance
 

Abstract

Without assuming any probabilistic price dynamics, we consider a 
frictionless financial market given by the Skorokhod space, on which 
some financial options are liquidly traded. In this model-free setting 
we show various pricing-hedging dualities and the analogue of the 
fundamental theorem of asset pricing. For this purpose we study the 
corresponding martingale optimal transport (MOT) problem: We obtain a 
dual representation of the Kantorovich functional (super-replication 
functional) defined for functions (financial derivatives) on the 
Skorokhod space using quotient sets (hedging sets). Our representation 
takes the form of a Choquet capacity generated by martingale measures 
satisfying additional constraints to ensure compatibility with the 
quotient sets. The talk is based on a joint work with Patrick 
Cheridito, Matti Kiiski and H. Mete Soner.

Dr. Ludovic TANGPI  (Princeton University)

30th of January

2:00 pm

LT 15

Roger Stevens Building

The talk by Dr. Ludovic Tangpi has been postponed to a later date.

Dr. Martin HERDEGEN  (University of Warwick)

13th of February

2:00 pm-3:00pm

LT 05 (7.05)

Roger Stevens

DOUBLE

SEMINAR

Title

A Dual Characterisation of Regulatory Arbitrage for Coherent Risk Measures

Abstract

We revisit portfolio selection in a one-period financial market under a coherent risk measure constraint, the most prominent example being Expected Shortfall (ES). Unlike in the case of classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage. We then show that the absence of regulatory arbitrage is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual characterisation of the risk measure. In the special case of ES, our result shows that the market does not admit regulatory arbitrage for ES at confidence level $\alpha$ if and only if there exists an EMM $Q \approx P$ such that $\Vert \frac{dQ}{dP} \Vert_\infty < \frac{1}{\alpha}$.

The talk is based on joint work with my PhD student Nazem Khan.

Prof. Johannes  MUHLE-KARBE  (Imperial College London)

13th of February

3:10 pm-4:10pm

LT 05 (7.05)

Roger Stevens

DOUBLE

SEMINAR

Title

Equilibrium asset pricing with frictions

Abstract

We study how the prices of assets depend on their “liquidity”, that is, the ease with which they can be traded. We show that equilibrium prices and the corresponding optimal trading strategies can be characterised by systems of coupled forward-backward SDEs. We outline some first wellposedness results and discuss explicit formulas that arise in the limit of large liquidity. 

 

The talk is based on joints works with Agostino Capponi, Lukas Gonon, Martin Herdegen, Dylan Possamai, and Xiaofei Shi.

Prof. Fausto  GOZZI  (University LUISS Rome )

20th of February

2:00 pm

LT 5

Roger Stevens Building

Title

From "simple" stochastic control problems to "more realistic" ones:
an example from portfolio theory

 

Abstract

In this talk we take an example from life-cycle portfolio theory
(modelled as a stochastic optimal control problem)
where we see how different economic questions, possibly arising from experimental data,
bring to formulate and study more complex problems, in particular
models which display path dependency and/or Mc Kean - Vlasov type dynamics.
Ongoing results on such problems will be presented.

We will discuss, depending on the available time, the following modelling levels.
Level 1: Lifecycle portfolio with Labor Income
Level 2: Lifecycle portfolio with Path-Dependent Labor Income  (History dependent wages)
Level 3/1: Lifecycle portfolio with Path-Dependent Labor Income with uncertainty on parameters
(Taking account of estimation errors)
Level 3/2: Lifecycle portfolio with Path-Dependent Labor Income with Mc Kean-Vlasov type dynamics
(Taking account of the effect of the environment: "Keeping up with the Joneses")

Based on joint papers/work in progress with various authors
( Biagini, Biffis, Cosso, Djeiche, Kharroubi, Pham, Prosdocimi, Rosestolato, Zanco, Zanella).

This talk has been CANCELLED.
 

Prof. Saul JACKA  (University of Warwick)

27th of February

2:00 pm

LT 5

Roger Stevens Building

Title

Minimising the shuttle/commute time

Abstract

We consider the problem of choosing a diffusion's drift so as to minimise the expected time to commute from zero to 1 and back again.

We solve this first as a static problem and then (in  a suitable sense) dynamically.

Prof. Zhenya LIU 

(University Aix-Marseille and Renmin University of China)

5th of March

2:00 pm

LT 6.142

Worsley Building

Title

The Optimal Equity Selling Price with Endogenous Drawdown

Abstract

In this paper, we propose the endogenous drawdown in an investor's reward function. The endogenous drawdown is the difference between the underlying process and its maximum related process. We find the optimal selling price is a function of the historical highest price, the weights of profit and loss in investor's reward function, and the characters of the underlying stochastic process. With the data of the S&P 500 Index and SSE Composite Index, we calculate the numerical solution of the optimal selling price with consideration of endogenous drawdown. Through the out-sample test, this optimal selling price performs well to sell before the price drops sharply.

Dr. Ankush AGARWAL  (University of Glasgow)

12th of March

2:00 pm

LT 5

Roger Stevens Building

Title

A Fourier-based Picard-iteration approach for a class of McKean-Vlasov SDEs with Lévy jumps

Abstract

We consider a prototype class of Lévy-driven stochastic  differential equations (SDEs) with McKean-Vlasov (MK-V) interaction in the drift coefficient. It is assumed that the drift coefficient is affine in the state variable, and only measurable in the law of the solution. We study the equivalent functional fixed-point equation for the unknown time-dependent coefficients of the associated linear Markovian SDE. By proving a contraction property for the functional map in a suitable normed space, we infer existence and uniqueness results for the MK-V SDE, and derive a discretized Picard iteration scheme that approximates the law of the solution through its characteristic function. Numerical illustrations show the effectiveness of our method, which appears to be appropriate to handle the multi-dimensional setting. This is a joint work with Stefano Pagliarani.

Prof. Tusheng ZHANG  (University of Manchester)

12th of March

3:10 pm

LT 5

Roger Stevens Building

Title

Abstract

Prof. Jacco  THIJSSEN  (University of York)

19th of March

2:00 pm-3:00pm

LT 5

Roger Stevens Building

Title

TBA

Abstract

TBA

DOUBLE SEMINAR

Prof. Peter BANK  (Technische Universität-Berlin)

19th of March

3:10 pm-4:10pm

LT 5

Roger Stevens Building

Title

TBA

Abstract

TBA

DOUBLE SEMINAR

Prof. Istvan GYÖNGY  (University of Edinburgh)

26th of March

2:00 pm-3:00pm

LT 5

Roger Stevens Building

Title

TBA

Abstract

TBA