Autumn 2024 @ King's College (Oct-Dec)
Date:
Thursday, October 10, 2024
Time: 16:00-17:00
Location: Room FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
John Armstrong (King's College London)
Title: Rough paths and gamma hedging
Abstract: We will show how the gamma-hedging trading strategy natural emerges from the theory of rough paths. Since rough-path theory is non-probabilistic, this gives sure convergence results for the discrete-time gamma-hedging strategy that depend only on the regularity of the signal. As an example, we show that European options can be replicated using the gamma-hedging strategy so long as the stock price process and the implied volatility process of the hedging option are sufficiently regular, but without any probabilistic assumptions on the signal. We will examine how these results generalize to path-dependent options.
Date: Thursday, October 10, 2024
Time: 17:00-18:00
Location: Room FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
Seyoung Park (Nottingham University Business School)
Title: Income Disaster Model with Optimal Consumption
Abstract: We propose a continuous-time income disaster model with optimal consumption. We endogenously determine the stochastic discount factor (SDF) in an incomplete market caused by income disaster. We then derive optimal consumption decisions for two types of agents, one who is exposed to income disaster and another who is not. We find a large incomplete-markets precautionary savings term between the two agents, which pushes the interest rate down and helps to resolve the risk-free rate puzzle. Interestingly, with income disaster the equilibrium interest rate is a decreasing function of risk aversion while the equity premium is an increasing function. Finally, our model can better match empirical marginal propensities to consume numbers and explain the low-consumption-high-savings puzzle.
Date: Thursday, October 24, 2024
Time: 16:00-17:00
Location: Room FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
Moris Strub (Warwick Business School)
Title: How to Choose a Model? A Consequentialist Approach Applied to Portfolio Selection in Continuous-Time
Abstract: We propose a consequentialist approach to model selection: Models should be chosen not according to statistical criteria, but in view of how they are used. This principle is then studied in detail for continuous-time portfolio choice. Specifically, we consider an econometrician with prior beliefs on the likelihood of models to transpire and faced with the task of communicating a single model to a client. The client then accepts the model communicated by the econometrician and invests according to the strategy that maximizes expected utility within this specific model. As a consequence, the client receives the consequential performance of trading according to the model communicated by the econometrician in a potentially different model which accurately describes the world. The objective of the econometrician is to choose the model that maximizes the consequential performance of the client, averaged over the likelihood of models to transpire and weighted according to the risk preferences of the econometrician. One of the key findings is that it is best to recommend a model that is more optimistic than an unbiased estimator would suggest. This presentation is based on joint work with Thaleia Zariphopoulou.
Date: Thursday, October 24, 2024
Time: 17:00-18:00
Location: Room FWB 1.70, Franklin Wilkins Building, KCL (Waterloo Campus)
Speaker:
Dylan Possamaï (ETH Zürich)
Title: A target approach to Stackelberg games
Abstract: In this paper, we provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a Stackelberg game in which the leader and the follower can both control the drift and the volatility of a stochastic output process, in order to maximise their respective expected utility. The aim is to characterise the Stackelberg equilibrium when the players adopt "closed-loop strategies", i.e. their decisions are based solely on the historical information of the output process, excluding especially any direct dependence on the underlying driving noise, often unobservable in real-world applications. We first show that, by considering the-second-order-backward stochastic differential equation associated with the continuation utility of the follower as a controlled state variable for the leader, the latter's unconventional optimisation problem can be reformulated as a more standard stochastic control problem with stochastic target constraints. Thereafter, adapting the methodology developed by Soner and Touzi or Bouchard, Élie, and Imbert, the optimal strategies, as well as the corresponding value of the Stackelberg equilibrium, can be characterised through the solution of a well-specified system of Hamilton–Jacobi–Bellman equations. For a more comprehensive insight, we illustrate our approach through a simple example, facilitating both theoretical and numerical detailed comparisons with the solutions under different information structures studied in the literature. This is a joint work with Camilo Hernández, Nicolás Hernández Santibáñez, and Emma Hubert.
Date: Thursday, November 7, 2024
Time: 16:00-17:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Nicole Baeuerle (Karlsruhe Institute of Technology)
Title: Optimal investment in ambiguous financial markets with learning
Abstract:
We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset prize realizations during the investment horizon. While the solution of an expected utility maximizing investor with constant relative risk aversion (CRRA) is well known, we consider the optimization problem under risk and ambiguity preferences by means of the KMM (Klibanoff, Marinacci and Mukerji, 2005) approach. Here, the investor maximizes a double certainty equivalent. The inner certainty equivalent is for given drift coefficient, the outer is based on a driftdistribution. Assuming also a CRRA type ambiguity function, it turns out that the optimal strategy can be stated in terms of the solution without ambiguity preferences but an adjusted drift distribution. We rely on some duality theorems to prove our statements. Based on our theoretical results, we are able to shed light on the impact of the prior drift distribution as well as the consequences of ambiguity preferences via the transfer to an adjusted drift distribution. We illustrate our findings with a numerical study. If time allows we will briefly discuss how these ideas can be used for other stochastic dynamic optimization problems. The talk is based on a joint work with Antje Mahayni.
Date: Thursday, November 7, 2024
Time: 17:00-18:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Hirbod Assa (University of Essex)
Title: Systematic Risk in Pools
Abstract: In the realm of portfolio diversification, the focus lies on constructing a well-diversified portfolio to mitigate unsystematic risk, allowing for the identification and measurement of systematic risk through uni-factor, CAPM, and multi-factor, APT, models. This approach is rooted in the belief that, with a sufficiently diversified portfolio, unsystematic risk in theory can be eliminated, making the remaining systematic risk more apparent. While diversification is the mean to diversify the unsystematic risk in a portfolio management problem, pooling strategies, with a limited strategy of just expanding the pool members, necessitate a distinct approach to systematic risk. In such scenarios, the challenge lies in disentangling the impact of systematic factors from idiosyncratic influences within a pool. This paper explores the methodologies and considerations unique to pooling situations, shedding light on the complexities involved in identifying and quantifying systematic risk in a pool. In our effort to assess the concept of systematic risk in a pool, we adopt an approach that identifies the defining characteristics of systematic risks, which remain invariant regardless of the number of losses or any manipulations within a finite set of losses. To explore these principles, we find a framework of risk management on sequences in Banach lattices to be particularly suitable. In establishing these principles, we introduce the notion of “systematic compatibility”, signifying invariance to variations in finite changes within a sequence of losses. Consequently, we observe that while systematic risk often possesses an implicit representation in the risk space, it exhibits an explicit representation in the bi-dual space. Moreover, we introduce systematic compatible risk measures and establish their dual characterization. We demonstrate that risk measurement can naturally be represented as a split into a summation of systematic and unsystematic components. In practical applications, we employ these measures to address risk management problems, with a specific emphasis on risk pooling scenarios. In revisiting the traditional “principle of insurance” (POI), we propose an extension called the “principle of pooling” (POP). By showing that the principle of pooling holds if and only if the systematic risk is secure, we investigate this novel concept.
Date: Thursday, November 21, 2024
Time: 16:00-17:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Mathias Beiglböck (University of Vienna)
Title: Non-linear transport theory and applications in finance.
Abstract: Gozlan, Roberto, Samson and Tetali introduced a non-linear relaxation of classical optimal
transport. On the one hand, this framework of weak optimal transport (WOT) still retains many characteristics of usual optimal transport, allowing for a compelling theory. On the other hand, this type of relaxation is suitable to cover a number of problems that lie outside the scope of the classical theory. We give a gentle introduction and discuss the applications to a number of challenges appearing in mathematical finance: this concerns the Bass local volatility model, pricing of VIX futures, robust pricing for fixed income markets and the optimal Skorokhod embedding problem.
Date: Thursday, November 21, 2024
Time: 17:00-18:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Tiziano De Angelis (University of Torino)
Title: Linear-quadratic stochastic control with state constraints on finite-time horizon
Abstract: We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal D\subseteq [0,T]\times\mathbb R^d$, a diffusion $X$ in $\mathbb R^d$ must be linearly controlled in order to keep the time-space process $(t,X_t)$ inside the set $\mathcal D^c:=([0,T]\times\mathbb R^d)\setminus\mathcal D$, while at the same time minimising an expected cost that depends on the state $(t,X_t)$ and it is quadratic in the speed of the control exerted.
We find an explicit probabilistic representation for the value function and the optimal control under a set of mild sufficient conditions concerning the coefficients of the underlying dynamics and the regularity of the set $\mathcal D^c$. Fully explicit formulae are presented in some relevant examples. (Joint work with Erik Ekström, University of Uppsala, Sweden).
Date: Thursday, December 5, 2024
Time: 16:00-17:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Nils Detering (Heinrich Heine University Düsseldorf)
Title: In-Context Operator Learning for Linear Propagator Models
Abstract: We study operator learning in the context of linear propagator models for optimal order execution problems with transient price impact \`a la Bouchaud et al. Bouchaud et al. (2004) and Gatheral~(2010). Transient price impact persists and decays over time according to some propagator kernel. Specifically, we propose to use In-Context Operator Networks (ICONs), a novel transformer-based neural network architecture introduced by Yang et al.~(2023), which facilitates data-driven learning of operators by merging offline pre-training with an online few-shot prompting inference. First, we train ICON to learn the operator from various propagator models that maps the trading rate to the induced transient price impact. The inference step is then based on in-context prediction, where ICON is presented only with a few examples. We illustrate that ICON is capable of accurately inferring the underlying price impact model from the data prompts, even with propagator kernels not seen in the training data. In a second step, we employ the pre-trained ICON model provided with context as a surrogate operator in solving an optimal order execution problem via a neural network control policy, and demonstrate that the exact optimal execution strategies from Abi Jaber and Neuman (2022) for these models generating the context are correctly retrieved.
Joint work with Tingwei Meng, Moritz Voss, Giulio Farolfi, Stanley Osher, and Georg Menz (UCLA).
Date: Thursday, December 5, 2024
Time: 17:00-18:00
Location: Room K-1.15 (Floor -1), King's Building, KCL (Strand Campus)
Speaker:
Claudia Ceci (University of Rome – La Sapienza)
Title: Optimal Self-Protection via BSDEs for risk models with jump clusters
Abstract: We investigate the optimal self-protection problem, from the point of view of an insurance buyer, when the loss process is described by a Cox-shot-noise process and a Hawkes process with an exponential memory kernel. The insurance buyer chooses both the percentage of insured losses and the prevention effort. The latter term refers to actions aimed at reducing the frequency of the claim arrivals. The problem consists in maximizing the expected exponential utility of terminal wealth, in presence of a terminal reimbursement. We show that this problem can be formulated in terms of a suitable backward stochastic differential equation (BSDE), for which we prove the existence and uniqueness of the solution. We extend in several directions the results obtained by Bensalem, Santibanez and Kazi-Tani [Finance Stoch. 2023] and compare our results with those presented therein. The talk is based on a joint paper with M. Brachetta, G. Callegaro and C. Sgarra.
Date: Thursday, December 12, 2024
Time: 17:00-18:00 (one talk only)
Location: Room CLM.3.02, LSE (Clement House, Aldwych)
Speaker:
Philip Protter (Columbia University)
Title: Dependent Stopping Time
Abstract: Often in subjects such as Credit Risk, one uses Reduced Form Models in place of Structural Models. In Reduced Form Models the stopping times of interest are totally inaccessible, and what is important is their compensators, which allow one to predict, in some sense, how likely they will be to occur imminently. These stopping times are typically constructed via a Cox Method of Construction, which works well most of the time. It leads to the attractive trait that two such constructed stopping times are conditionally independent, given the underlying filtration. In some situations, however, we wish not to have the property of conditional independence. This is particularly important in predicting catastrophic events, such as the simultaneous systemic failure of two or more globally important banks/financial houses. This talk will extend the usual Credit Risk Theory to dependent, and not conditionally independent, failure times. This part of the talk is based on joint work with Alejandra Quintos. In work with Andrés Riveros, we show the Cox construction—which seems a bit ad hoc and artificial, is actually intrinsic to the jump times of strong Markov Feller processes
Winter 2024 @ Imperial (Jan-Mar)
Date: Thursday,
January 18, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Jean-Paul Decamps, Université Toulouse Capitole
Title: The War of Attrition under Uncertainty: Theory and robust testable implications
Abstract: We study the war of attrition with symmetric information when players' payoffs depend on a homogeneous linear diffusion. We first show that a player's mixed Markov strategy can be represented by an intensity measure over the state space along with a subset of the state space over which the player concedes with probability 1. We then show that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, these intensity measures must be discrete, and characterize any such equilibrium through a variational system for the players' value functions. We illustrate these findings by revisiting the standard model of exit in a duopoly under uncertainty and construct a mixed-strategy Markov-perfect equilibrium in which attrition takes place on path despite firms having different liquidation values. We show that firms' stock prices comove negatively over the attrition zone and exhibit patterns documented by technical analysis. Joint work with Fabien Gensbittel and Thomas Mariotti.
Date: Thursday, January 18, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Zbigniew Palmowski, Wroclaw University of Science and Technology
Title: Cancellable American options under negative discounting
Abstract: Cancellable American options, also known as game options or Israeli options, are American-style derivatives which give the writer the right to terminate the contract for a fixed penalty. I will talk about perpetual cancellable American put options on an asset whose dynamics follow exponential spectrally negative Lévy process. The price and optimal strategies of the buyer and the writer can be deduced from the solution of a corresponding Dynkin game. The new feature of the model is the negative interest rate which brings in difficulties (the payoff grows exponentially fast in time) and interesting strategies. We employ fully probabilistic arguments to argue the existence of the value and of the optimal strategies and characterise explicitly their form. We also prove smooth fit at boundaries of stopping sets enabling their numerical identification. The talk is based on the joint work with Jan Palczewski.
Date: Thursday,
February 1, 2024
Time:
16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Julien Guyon, Ecole des Ponts ParisTech
Title: Fast exact joint S&P 500/VIX smile calibration in discrete and continuous time
Abstract: We introduce a novel discrete-time-continuous-time exact calibration method: we first build an S&P 500/VIX jointly calibrating discrete-time model that is later extended to continuous time by martingale interpolation. The benefit is that both steps can be made much faster than the known methods that directly calibrate a continuous-time model. We propose Newton--Sinkhorn and implied Newton algorithms that are much faster than the Sinkhorn algorithm that (Guyon, Risk, April 2020) used to build the first arbitrage-free model exactly consistent with S&P 500 and VIX market data. Using a (purely forward) Markov functional model, we then quickly build an arbitrage-free continuous-time extension of this discrete-time model. Additionally, new model-free bounds on S&P 500 options emphasize the value of the VIX smile information. Extensive numerical tests are conducted. This is joint work with Florian Bourgey (Bloomberg).
Date: Thursday, February 1, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Christian Bayer, Weierstrass Institute
Title: Primal and dual optimal stopping with signatures
Abstract: We propose two signature-based methods to solve the optimal stopping problem - that is, to price American options - in non-Markovian frameworks. Both methods rely on a global approximation result for Lp−functionals on rough path-spaces, using linear functionals of robust, rough path signatures. In the primal formulation, we present a non-Markovian generalization of the famous Longstaff-Schwartz algorithm, using linear functionals of the signature as regression basis. For the dual formulation, we parametrize the space of square-integrable martingales using linear functionals of the signature, and apply a sample average approximation. We prove convergence for both methods and present first numerical examples in non-Markovian and non-semimartingale regimes. (Joint work with Luca Pelizzaru and John Schoenmakers.)
Date: Thursday, February 15, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Miryana Grigorova, University of Warwick
Title: Optimal stopping and non-zero-sum games: Bermudan strategies meet non-linear evaluations
Abstract: We address an optimal stopping problem over the set of Bermudan-type stopping strategies (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with non-linear operators (non-linear evaluations) assessing the rewards, under general assumptions on the non-linear operators. We provide a characterization of the value family V in terms of a suitably defined non-linear Snell envelope of the pay-off family. We establish a Dynamic Programming Principle. We provide an optimality criterion in terms of a non-linear martingale property of V on a stochastic interval. We investigate the non-linear martingale structure and we show that, under suitable conditions, the first time when the value family coincides with the pay-off family is optimal. The reasoning simplifies in the case where there is a finite number, say n, of pre- described stopping times, where n does not depend on the state of nature. We will also discuss a non-zero-sum non-linear game with Bermudan stopping strategies, for which we show the existence of a Nash equilibrium point, via a recursive procedure. We provide examples of non-linear operators from the stochastic control and mathematical finance literature, which enter our framework. The talk is based on an ongoing joint works with Marie-Claire Quenez (Paris) and Peng Yuan (Warwick).
Date: Thursday, February 15, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Nikolas Nüsken, King's College London
Title: Optimal control of diffusions, forward-backward stochastic differential equations, and variational inference.
Abstract: The aim of this talk is to present a few recent ideas at the interface of optimal control and machine learning: The core challenge in computational Bayesian statistics is the approximation of probability measures, and when those are considered on path space, many fruitful connections between variational inference and stochastic optimal control emerge. No prior knowledge of variational inference is required – I will give an introduction and point out connection and equivalences.
Date: Thursday, February 29, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Olivier Guéant, Université Paris 1 Panthéon-Sorbonne
Title:
Incorporating Variable Liquidity in Optimal Market Making and
Inventory Management Models: A Comparison of Hawkes Processes and
Markov-Modulated Poisson Processes
Abstract: Since Avellaneda and Stoikov's seminal work, market making models have evolved to incorporate increasingly realistic aspects, such as complex price dynamics, price differentiation, adverse selection, or even parameter ambiguity. However, the dynamics of liquidity have been less frequently addressed. While Hawkes processes are a natural choice for modelling beyond constant request and trade intensities, this talk introduces an alternative approach using Markov-modulated Poisson processes (MMPPs). We will explore the benefits and limitations of MMPPs and Hawkes processes in the context of algorithmic market making and inventory management model development.
Date: Thursday, February 29, 2024
Time: 17:00-18:00
Location:
Imperial College London, Huxley Building, Room 140
Speaker: Lyudmila Grigoryeva, University of St. Gallen
Title: Reservoir kernels and Volterra series
Abstract:
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir functional associated with a state-space representation of the Volterra series expansion available for any analytic fading memory filter. It is hence called the Volterra reservoir kernel. Even though the state-space representation and the corresponding reservoir feature map are defined on an infinite-dimensional tensor algebra space, the kernel map is characterized by explicit recursions that are readily computable for specific data sets when employed in estimation problems using the representer theorem. We showcase the performance of the Volterra reservoir kernel in a popular data science application in relation to bitcoin price prediction.
Date: Thursday, March 14, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Aurélien Alfonsi, Ecole des Ponts ParisTech
Title: Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation.
Abstract: We define and study convolution kernels that preserve nonnegativity. When the past dynamics of a process is integrated with a convolution kernel like in Stochastic Volterra Equations or in the jump intensity of Hawkes processes, this property allows to get the nonnegativity of the integral. We give characterizations of these kernels and show in particular that completely monotone kernels preserve nonnegativity. We then apply these results to analyze the stochastic invariance of a closed convex set by Stochastic Volterra Equations. We also get a comparison result in dimension one. Last, when the kernel is a positive linear combination of decaying exponential functions, we present a second order approximation scheme for the weak error that stays in the closed convex domain under suitable assumptions. We apply these results to the rough Heston model and give numerical illustrations.
Date: Thursday, March 14, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Walter Schachermayer, University of Vienna
Title: Martingale Transports in R^n
Abstract: A remarkable theorem of Backhoff-Beiglboeck-Huesman-Kaellblad shows that between probabilities \mu, \nu on R^n which are in convex order and have finite second moments, there always is a unique martingale transport termed “stretched Brownian motion” from \mu to \nu. This transport enjoys many nice properties. A special subclass - with even nicer properties - are termed “Bass martingales”: R. Bass used a similar construction some forty years ago in the context of the Skorohod embedding problem.
We show a necessary and sufficient condition for a stretched Brownian motion to be a Bass martingale, namely irreducibility of the pair (\mu,\nu). The intuitive content of the notion of irreducibility is that there no non-trivial subset of R^n which is invariant under all martingale transports from \mu to \nu.
In the general case, i.e. without imposing irreducibility, we show that the stretched Brownian motion can be decomposed into a family of Bass martingales. This makes contact with previous work by DeMarch-Touzi and Obloj-Siorpaes, as this decomposition generates the universal paving of R^d into invariant sets.
Date: Wednesday, March 27, 2024
Time: 16:00-17:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Sören Christensen, Christian-Albrechts University Kiel
Title: How to Learn from Data in Stochastic Control Problems - An Approach Based on Statistics
Abstract: While theoretical solutions to many stochastic control problems are well understood, their practicality often suffers from the assumption of known dynamics of the underlying stochastic process, which raises the statistical challenge of developing purely data-driven controls. In this talk, we discuss how stochastic control and statistics can be brought together, which we study for various classical control problems with underlying one- and multi-dimensional diffusions and jump processes. The dilemma between exploration and exploitation plays an essential role in the considerations. We find exact sublinear-order convergence rates for the regret and compare the results numerically with those of deep Q-learning algorithms.
Date: Wednesday, March 27, 2024
Time: 17:00-18:00
Location: Imperial College London, Huxley Building, Room 140
Speaker: Peter Tankov, ENSAE
Title: Asset pricing under transition scenario uncertainty and model ambiguity
Abstract: We study asset pricing and optimal investment decisions for an economic agent whose future revenues depend on the realization of a scenario from a given set of possible futures. In the first part of the talk, we assume that future scenario is unknown, but that the possible scenarios have equal probabilities, and the agent deduces scenario information progressively by observing a signal. The problem of valuing an investment is formulated as an American option pricing problem with Bayesian learning. In the second part, we assume that the probabilities of individual prospective scenarios are ambiguous and place ourselves into the smooth model of decision making under ambiguity aversion of Klibanoff et al (2005), framing the optimal investment decision as an optimal stopping problem with learning under ambiguity. We then prove a minimax result allowing to reduce this problem to a series of standard optimal stopping problems. The theory is illustrated with two examples: the problem of optimally selling a stock with ambiguous drift, and the problem of optimal divestment from a coal-fired power plant under transition scenario ambiguity.
