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Autumn Semester 2021

Date / Time Speaker Title Location
23 September 2021
17:15-18:15 		Prof. Dr. Mathias Beiglböck
University of Vienna
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Talks in Financial and Insurance Mathematics

Title The Wasserstein Space of Stochastic Processes
Speaker, Affiliation Prof. Dr. Mathias Beiglböck, University of Vienna
Date, Time 23 September 2021, 17:15-18:15
Location HG G 43
Abstract Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied mathematics. We believe that an appropriate probabilistic variant, the adapted Wasserstein distance $AW$, can play a similar role for the class $FP$ of filtered processes, i.e. stochastic processes together with a filtration. In contrast to other topologies for stochastic processes, probabilistic operations such as the Doob-decomposition, optimal stopping and stochastic control are continuous w.r.t. $AW$. We also show that $(FP, AW)$ is a geodesic space, isometric to a classical Wasserstein space, and that martingales form a closed geodesically convex subspace.
The Wasserstein Space of Stochastic Processesread_more
HG G 43
30 September 2021
17:15-18:15 		Prof. Dr. Walter Schachermayer
University of Vienna
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Talks in Financial and Insurance Mathematics

Title The Duality Theory of Stretched Brownian Motion
Speaker, Affiliation Prof. Dr. Walter Schachermayer, University of Vienna
Date, Time 30 September 2021, 17:15-18:15
Location HG G 43
Abstract We continue the investigation of martingale transports from a measure $\mu$ to a measure $\nu$ on $\R^d$. The notion of stretched Brownian motion, as introduced by Backhoff, Beiglböck, Huesmann, and Källblad, can be defined as the solution to this problem which is “closest to Brownian motion”. We develop further the duality theory attached to this concept. As an application we show that in the case of a single invariant deMarch-Touzi component the stretched Brownian motion is of standard type. Joint work with Backhoff, Beiglböck, and Tschiderer.
The Duality Theory of Stretched Brownian Motionread_more
HG G 43
7 October 2021
17:15-18:15 		Prof. Dr. Mathieu Rosenbaum
École Polytechnique
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Talks in Financial and Insurance Mathematics

Title AHEAD : Ad-Hoc Electronic Auction Design
Speaker, Affiliation Prof. Dr. Mathieu Rosenbaum, École Polytechnique
Date, Time 7 October 2021, 17:15-18:15
Location HG G 43
Abstract We introduce a new matching design for financial transactions in an electronic market. In this mechanism, called ad-hoc electronic auction design (AHEAD), market participants can trade between themselves at a fixed price and trigger an auction when they are no longer satisfied with this fixed price. In this context, we prove that a Nash equilibrium is obtained between market participants. Furthermore, we are able to assess quantitatively the relevance of ad-hoc auctions and to compare them with periodic auctions and continuous limit order books. We show that from the investors' viewpoint, the microstructure of the asset is usually significantly improved when using AHEAD. This is joint work with Joffrey Derchu, Philippe Guillot and Thibaut Mastrolia.
AHEAD : Ad-Hoc Electronic Auction Designread_more
HG G 43
7 October 2021
18:15-19:15 		Prof. Dr. Sebastian Jaimungal
University of Toronto
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Talks in Financial and Insurance Mathematics

Title Deep Learning for Principal-Agent Mean Field Games with Applications to Renewable Energy
Speaker, Affiliation Prof. Dr. Sebastian Jaimungal, University of Toronto
Date, Time 7 October 2021, 18:15-19:15
Location HG G 43
Abstract In this talk, I will discuss an approach for solving principal-agent problems with many (heterogeneous) players, and market clearing, using deep learning – a class of problems otherwise intractable. The problem is broken into two stages: (i) how the individual agents react and form a Nash equilibria given a particular cost/reward imposed by the principal, and (ii) how the principal then selects the optimal cost/reward, knowing that the agents act optimally. Using a variational approach, we first cast the agents’ problem, which also includes market clearing, into a system of MV-FBSDE. This MV-FBSDE is then approximately solved using ideas from deep learning. The principal then obtains local approximations to its performance criterion and takes gradient steps to an optimal. I will illustrate some numerical results on a stylized renewable energy certificate market where the agents may rent capacity, expand their capacity, and trade certificates. This is joint work with Dena Firoozi, Arvind Shrivats, Yichao Chen, and Steven Campbell.
Deep Learning for Principal-Agent Mean Field Games with Applications to Renewable Energyread_more
HG G 43
14 October 2021
17:15-18:15 		Dr. Anastasis Kratsios
University of Basel
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Talks in Financial and Insurance Mathematics

Title Universal Approximation under Constraints is Possible with Transformers
Speaker, Affiliation Dr. Anastasis Kratsios, University of Basel
Date, Time 14 October 2021, 17:15-18:15
Location HG G 43
Abstract Many practical problems need the output of a machine learning model to satisfy a set of constraints, K. Nevertheless, there is no known guarantee that classical neural network architectures can exactly encode constraints while simultaneously achieving universality. We provide a quantitative constrained universal approximation theorem which guarantees that for any non-convex compact set K and any continuous function f:Rn→K, there is a probabilistic transformer F whose randomized outputs all lie in K and whose expected output uniformly approximates f. Our second main result is a "deep neural version" of Berge's Maximum Theorem (1963). The result guarantees that given an objective function L, a constraint set K, and a family of soft constraint sets, there is a probabilistic transformer F that approximately minimizes L and whose outputs belong to K; moreover, F approximately satisfies the soft constraints. Our results imply the first universal approximation theorem for classical transformers with exact convex constraint satisfaction. They also yield that a chart-free universal approximation theorem for Riemannian manifold-valued functions subject to suitable geodesically convex constraints. Joint work with Behnoosh Zamanlooy, Ivan Dokmanić and Tianlin Liu.
Universal Approximation under Constraints is Possible with Transformersread_more
HG G 43
21 October 2021
17:15-18:15 		Dr. Philippe Casgrain
ETH Zurich, Switzerland
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Talks in Financial and Insurance Mathematics

Title Anytime-valid Sequential Testing for Elicitable Functionals via Supermartingales
Speaker, Affiliation Dr. Philippe Casgrain, ETH Zurich, Switzerland
Date, Time 21 October 2021, 17:15-18:15
Location HG G 43
Abstract We consider the problem of testing statistical hypotheses and building confidence sequences for elicitable and identifiable functionals, a broad class of statistical quantities which are of particular interest in the field of quantitative risk management. Assuming a framework in which data is collected sequentially, where a user may choose to accept or reject a hypothesis at any point in time, we provide powerful distribution-free and anytime-valid testing methods which rely on controlled supermartingales. Leveraging tools from online convex optimization, we show that tests can be optimized to improve their statistical power, with asymptotic guarantees for rejecting false hypotheses. By "inverting the test", these methods are extended to the task of confidence sequence building. Lastly, we implement these techniques on a range of examples to demonstrate their effectiveness.
Anytime-valid Sequential Testing for Elicitable Functionals via Supermartingalesread_more
HG G 43
28 October 2021
17:15-18:15 		Prof. Dr. David Prömel
Universität Mannheim
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Talks in Financial and Insurance Mathematics

Title Model-free Portfolio Theory: A Rough Path Approach
Speaker, Affiliation Prof. Dr. David Prömel, Universität Mannheim
Date, Time 28 October 2021, 17:15-18:15
Location HG G 43
Abstract Classical approaches to optimal portfolio selection problems are based on probabilistic models for the asset returns or prices. However, by now it is well observed that the performance of optimal portfolios are highly sensitive to model misspecifications. To account for various types of model risk, robust and model-free approaches have gained more and more importance in portfolio theory. Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory and Cover's universal portfolio. The use of rough path theory allows to treat significantly more general portfolios in a model-free setting, compared to previous model-free approaches. Without the assumption of any underlying probabilistic model, we present pathwise Master formulae analogously to the classical ones in stochastic portfolio theory, describing the growth of wealth processes generated by pathwise portfolios relative to the market portfolio, and we show that the appropriately scaled asymptotic growth rate of Cover's universal portfolio is equal to that of the best retrospectively chosen portfolio. The talk will be given jointly with Andrew Allan, based on work with Christa Cuchiero and Chong Liu.
Model-free Portfolio Theory: A Rough Path Approachread_more
HG G 43
4 November 2021
17:15-18:15 		Prof. Dr. Hansjörg Albrecher
Université de Lausanne
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Talks in Financial and Insurance Mathematics

Title On the Profitability of Selfish Blockchain Mining under Consideration of Ruin
Speaker, Affiliation Prof. Dr. Hansjörg Albrecher, Université de Lausanne
Date, Time 4 November 2021, 17:15-18:15
Location HG G 43
Abstract Mining blocks on a blockchain equipped with a proof of work consensus protocol is known to be resource-consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining, and is compensated by a capital gain when a block is discovered. In this talk we quantify the profitability of mining when the possible event of ruin is also taken into consideration. This is done by formulating a tractable stochastic model and using tools from actuarial ruin theory and analysis, including the explicit solution of a certain type of advanced functional differential equation. The expected profit at a future time point is determined for the situation when the miner follows the protocol as well as when he/she withholds blocks. The obtained explicit expressions allow to analyze the sensitivity with respect to the different model ingredients and to identify conditions under which selfish mining is a strategic advantage. The talk is based on joint work with P.O. Goffard.
On the Profitability of Selfish Blockchain Mining under Consideration of Ruinread_more
HG G 43
11 November 2021
17:15-18:15 		Dr. Gudmund Pammer
ETH Zurich, Switzerland
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Talks in Financial and Insurance Mathematics

Title Faking Brownian Motion with Continuous Markov Martingales
Speaker, Affiliation Dr. Gudmund Pammer, ETH Zurich, Switzerland
Date, Time 11 November 2021, 17:15-18:15
Location HG G 43
Abstract Hamza and Klebaner posed the problem of constructing martingales with Brownian marginals that differ from Brownian motion, so-called fake Brownian motions. Besides its theoretical appeal, the problem represents the quintessential version of the ubiquitous fitting problem in mathematical finance, where the task is to construct martingales which satisfy marginal constraints imposed by market data. In the past 20 years, numerous mathematicians have constructed solutions to this challenge which are either non-continuous (and strongly Markovian) or continuous (but non-Markovian). In contrast, it is known from Gyöngy, Dupire, and ultimately Lowther that Brownian motion is the unique continuous strong Markov martingale with Brownian marginals. We took this as a challenge to construct examples of a ''very fake'' Brownian motion, that is, continuous Markov martingales with Brownian marginals that miss out only on the strong Markov property.
Faking Brownian Motion with Continuous Markov Martingalesread_more
HG G 43
18 November 2021
17:15-18:15 		Prof. Dr. Sergio Pulido
ENSIIE
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Talks in Financial and Insurance Mathematics

Title American Options in the Rough Heston Model
Speaker, Affiliation Prof. Dr. Sergio Pulido, ENSIIE
Date, Time 18 November 2021, 17:15-18:15
Location HG G 43
Abstract Rough volatility models have emerged as compelling alternatives to classical semimartingale models to capture important stylized features of the implied volatility surface and the time series of realized volatility. The rough Heston model is particularly appealing because its affine structure facilitates the pricing of European options using Fourier techniques. In this work we consider the problem of pricing American options in the rough Heston model. The complexity of the problem stems from the absence of a Markovian-semimartingale structure in the model. To overcome this difficulty we work with a Markovian multi-factor semimartingale stochastic volatility model, which approximates the rough Heston model. In this approximated model, American options can be priced using a backward approach and simulation-based methods. We prove the convergence of American options prices in the multi-factor model towards the prices in the rough Heston model. The proof relies on the explicit expression of the conditional characteristic function of the joint forward process and the spot price, which is a consequence of the affine structure of the model. We illustrate with some numerical examples the behavior of American option prices with respect to some parameters in the model. This is joint work with Etienne Chevalier and Elizabeth Zuniga.
American Options in the Rough Heston Modelread_more
HG G 43
25 November 2021
17:15-18:15 		Prof. Dr. Agostino Capponi
Columbia University
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Talks in Financial and Insurance Mathematics

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Agostino Capponi, Columbia University
Date, Time 25 November 2021, 17:15-18:15
Location
Title T.B.A. (CANCELLED)
2 December 2021
17:15-18:15 		Dr. Tobias Fissler
WU Vienna
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Talks in Financial and Insurance Mathematics

Title Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability
Speaker, Affiliation Dr. Tobias Fissler, WU Vienna
Date, Time 2 December 2021, 17:15-18:15
Location HG G 43
Abstract Backtesting risk measure forecasts requires identifiability (for model validation) and elicitability (for model comparison). The systemic risk measures CoVaR (conditional value-at-risk), CoES (conditional expected shortfall) and MES (marginal expected shortfall), measuring the risk of a position Y given that a reference position X is in distress, fail to be identifiable and elicitable. We establish the joint identifiability of CoVaR, MES and (CoVaR, CoES) together with the value-at-risk (VaR) of the reference position X, but show that an analogue result for elicitability fails. The novel notion of multi-objective elicitability however, relying on multivariate scores equipped with an order, leads to a positive result when using the lexicographic order on R^2. We establish comparative backtests of Diebold-Mariano type for superior systemic risk forecasts and comparable VaR forecasts, accompanied by a traffic-light approach. We demonstrate the viability of these backtesting approaches in an empirical application to DAX 30 and S&P 500 returns. The talk is based on the preprint https://arxiv.org/abs/2104.10673 which is joint work with Yannick Hoga.
Backtesting Systemic Risk Forecasts using Multi-Objective Elicitabilityread_more
HG G 43
9 December 2021
17:15-18:15 		Prof. Dr. Christa Cuchiero
University of Vienna
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Talks in Financial and Insurance Mathematics

Title Optimal Bailout Strategies Resulting from the Drift Controlled Supercooled Stefan Problem
Speaker, Affiliation Prof. Dr. Christa Cuchiero, University of Vienna
Date, Time 9 December 2021, 17:15-18:15
Location HG G 43
Abstract We consider the problem faced by a central bank which bails out distressed financial institutions that pose systemic risk to the banking sector. In a structural default model with mutual obligations, the central agent seeks to inject a minimum amount of cash to a subset of the entities in order to limit defaults to a given proportion of entities. We prove that the value of the agent's control problem converges as the number of defaultable agents goes to infinity, and that it satisfies a drift controlled version of the supercooled Stefan problem. We compute optimal strategies in feedback form by solving numerically a forward-backward coupled system of PDEs. Our simulations show that the agent's optimal strategy is to subsidise banks whose asset values lie in a non-trivial time-dependent region. Finally, we study a linear-quadratic version of the model where instead of the terminal losses, the agent optimises a terminal cost function of the equity values. In this case, we are able to give semi-analytic strategies, which we again illustrate numerically. The talk is based on joint work with Christoph Reisinger and Stefan Rigger.
Optimal Bailout Strategies Resulting from the Drift Controlled Supercooled Stefan Problemread_more
HG G 43
16 December 2021
17:15-18:15 		Prof. Dr. Kavita Ramanan
Brown University
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Talks in Financial and Insurance Mathematics

Title Beyond Mean-Field Limits: Marginal Dynamics of Interacting Particle Systems on Sparse Graphs
Speaker, Affiliation Prof. Dr. Kavita Ramanan, Brown University
Date, Time 16 December 2021, 17:15-18:15
Location Zoom
Abstract Homogeneously interacting particles systems in which the infinitesimal evolution of each particle depends on the states of neighbouring particles with respect to an underlying interaction graph model have a wide variety of applications in statistical physics, neuroscience, engineering and operations research. It is well known that when the graph is complete, the marginal dynamics of a typical particle is described by a mean-field limit. We consider the complementary case when the underlying graph is (a possibly random) sparse graph and describe novel characterizations of the limit empirical measure and marginal dynamics. This is joint work with A. Ganguly.
Beyond Mean-Field Limits: Marginal Dynamics of Interacting Particle Systems on Sparse Graphsread_more
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