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Frühjahrssemester 2021

Datum / Zeit Referent:in Titel Ort
25. Februar 2021
17:00-18:00 		Prof. Dr. Thibaut Mastrolia
École Polytechnique
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Talks in Financial and Insurance Mathematics

Titel Some Recent Developments of Auction Design in Financial Markets
Referent:in, Affiliation Prof. Dr. Thibaut Mastrolia, École Polytechnique
Datum, Zeit 25. Februar 2021, 17:00-18:00
Ort Zoom
Abstract We model sequential auctions in financial markets during a given time period receiving orders of market participants. A clearing price of the auction is determined as the price maximizing the exchanged volume at the clearing time according to the supply and demand of each market participants. We then focus on the optimal duration of an auction to reduce the error between the clearing price and the efficient price of the stock considered. When investors are strategical, they minimize simultaneously their transaction costs by adapting their trading intensities to the market state. We thus provide the existence of a Nash equilibrium for this stochastic game. We then compute the optimal duration of the auctions for some stocks traded on Euronext and compare the quality of price formation process under this optimal value to the case of a continuous limit order book. Finally, we extend the study to a new market mechanism interpolating CLOB and sequential auctions "ad hoc electronic auction design" AHEAD in which market participants have the opportunity to trigger the auction when necessary in addition to control their trading intensities. We prove in particular that this model is well-posed and we compare it with classical sequential auctions and limit order books.
Some Recent Developments of Auction Design in Financial Marketsread_more
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4. März 2021
17:00-18:00 		Prof. Dr. Soumik Pal
University of Washington
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Talks in Financial and Insurance Mathematics

Titel A Gibbs Measure Perspective on Schrodinger Bridges and Entropy Regularized Optimal Transport
Referent:in, Affiliation Prof. Dr. Soumik Pal, University of Washington
Datum, Zeit 4. März 2021, 17:00-18:00
Ort Zoom
Abstract Consider the problem of matching two independent sets of N i.i.d. observations from two densities. Such matchings correspond to the set of permutations of N labels. For an arbitrary continuous cost function, the optimal assignment problem looks for that permutation that minimizes the total cost of matching each pair of atoms. The empirical distribution of the matched atoms is known to converge to the solution of the Monge-Kantorovich optimal transport problem. Suppose instead we take a weighted convex combination of the empirical distribution of every matching, weighted proportional to the exponential of their (negative) total cost. Then the resulting distribution converges to the solution of a variational problem called the entropy-regularized optimal transport. The variational problem was introduced by Follmer in the late 80's trying to answer a question raised by Schrodinger on lazy gases. More recently, a beautiful circle of ideas connect this same object to Wasserstein gradient flows as well as faster numerical computations of optimal transport maps. As a big picture, we will discuss how discrete optimal transport problems can be analyzed by classical probabilistic tools such as exchangeability, U-statistics, and combinatorics of symmetric functions. This avoids the use of analytical machinery on metric measure spaces that are frequently used in such problems for the quadratic cost but are unavailable outside the Wasserstein spaces.
A Gibbs Measure Perspective on Schrodinger Bridges and Entropy Regularized Optimal Transportread_more
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11. März 2021
17:00-18:00 		Prof. Dr. Christian Robert
ISFA Lyon
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Talks in Financial and Insurance Mathematics

Titel Conditional Mean Risk Sharing in the Individual Model with Graphical Dependencies
Referent:in, Affiliation Prof. Dr. Christian Robert, ISFA Lyon
Datum, Zeit 11. März 2021, 17:00-18:00
Ort Zoom
Abstract Conditional mean risk sharing appears to be effective to distribute total losses among participants within an insurance pool. This paper develops analytical results for this allocation rule in the individual risk model with dependence induced by the respective position within a graph. Precisely, losses are modeled by zero-augmented random variables whose joint occurrence distribution and individual claim amount distributions are based on network structures and can be characterized by graphical models. The Ising model is adopted for occurrences and loss amounts obey decomposable graphical models that are specific to each participant. Two graphical structures are thus used: a first one to describe the contagion among member units within the insurance pool and a second one to model the spread of losses inside each participating unit. The proposed individual risk model is typically useful for modeling operational risks, catastrophic risks or cyber security risks.
Conditional Mean Risk Sharing in the Individual Model with Graphical Dependenciesread_more
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18. März 2021
17:00-18:00 		Dr. Andreas Søjmark
Imperial College London
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Talks in Financial and Insurance Mathematics

Titel Dynamic Default Contagion and Contagious McKean-Vlasov Systems
Referent:in, Affiliation Dr. Andreas Søjmark, Imperial College London
Datum, Zeit 18. März 2021, 17:00-18:00
Ort Zoom
Abstract In this talk I will present a simple framework for modelling contagion in heterogenous interbank networks, and we will then see how this can be formulated as a McKean-Vlasov problem under quite reasonable structural assumptions on the interactions. Depending on the initial profile of the system, one may have to face jump discontinuities emerging as instantaneous default cascades of macroscopic smite. The characterisation of such jumps from the symmetric case does not immediately look welcoming to heterogeneity, but we derive a different condition, which is equivalent in the symmetric case and extends naturally to our heterogenous setting. Additionally, this condition serves to more clearly capture the interpretation as a mean-field cascade. The talk is based on joint work with Zach Feinstein (some of which is ongoing, and some of which is from arXiv:1912.08695).
Dynamic Default Contagion and Contagious McKean-Vlasov Systemsread_more
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25. März 2021
17:00-18:00 		Prof. Dr. Filip Lindskog
Stockholm University
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Talks in Financial and Insurance Mathematics

Titel Market-Consistent Multiple-Priors Valuation of Cash Flows Subject to Capital Requirements
Referent:in, Affiliation Prof. Dr. Filip Lindskog, Stockholm University
Datum, Zeit 25. März 2021, 17:00-18:00
Ort Zoom
Abstract We study market-consistent valuation of liability cash flows subject to repeated capital requirements motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple prior optimal stopping we propose a valuation functional with sound economic properties that applies to any liability cash flow. For instance, whereas a replicable cash flows is assigned the market value of the replicating portfolio, a cash flow that is not replicable can be assigned a value which can be interpreted as a best estimate plus a risk margin. The latter implies conditions on the conditional risk measures defining capital requirements and on the set of probability measures, priors, defining the valuation functional. Aiming for applicability, we explain how the optimisation problems over sets of probability measures can be cast as simpler optimisation problems over parameter sets corresponding to parameterised density processes appearing in applications.
Market-Consistent Multiple-Priors Valuation of Cash Flows Subject to Capital Requirementsread_more
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1. April 2021
17:00-18:00 		Dr. Maria Flora
ENSAE, Institut Polytechnique de Paris
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Talks in Financial and Insurance Mathematics

Titel V-shapes
Referent:in, Affiliation Dr. Maria Flora, ENSAE, Institut Polytechnique de Paris
Datum, Zeit 1. April 2021, 17:00-18:00
Ort Zoom
Abstract An insidious form of market inefficiency, by which prices lose their informativeness and wealth is distributed arbitrarily, translates into V-shapes, that is sudden changes of the sign of the price drift. We use this insight to develop a new tool for the detection of reverting drift, the V-statistic. We apply this tool to (i) quantify the extent of this kind of market inefficiency in the U.S. stock market during the Covid-19 pandemic; and (ii) show the harmful consequences of V-shapes on financial stability by estimating the huge loss suffered by Italian taxpayers (0.45B euros) in May 2018, when a transient crash hit the secondary bond market during a Treasury auction.
V-shapesread_more
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8. April 2021
17:00-18:00
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Talks in Financial and Insurance Mathematics

Titel No seminar (Easter break)
Referent:in, Affiliation
Datum, Zeit 8. April 2021, 17:00-18:00
Ort
No seminar (Easter break)
15. April 2021
17:00-18:00 		Prof. Dr. Tiziano De Angelis
University of Turin
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Talks in Financial and Insurance Mathematics

Titel Dynkin Games with Partial and Asymmetric Information
Referent:in, Affiliation Prof. Dr. Tiziano De Angelis, University of Turin
Datum, Zeit 15. April 2021, 17:00-18:00
Ort Zoom
Abstract I will review some recent results obtained in collaboration with Ekström, Glover, Merkulov and Palczewski concerning existence of equilibria for Dynkin games with partial and asymmetric information. I will present a general result for the existence of a saddle point in zero-sum non-Markovian Dynkin games. Then I will illustrate explicit solutions to two specific problems: a zero-sum game with asymmetric information on the drift of a geometric Brownian motion and a non-zero sum game with uncertain competition. The construction of all equilibria relies upon the use of randomised stopping times. The talk is based on https://arxiv.org/abs/1810.07674 (Math. Oper. Res. 2020, to appear) https://arxiv.org/abs/1905.06564 (Stoch. Process. Appl. 130 (2020), pp. 6133-6156) https://arxiv.org/abs/2007.10643
Dynkin Games with Partial and Asymmetric Informationread_more
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22. April 2021
17:00-18:00 		Prof. Dr. Julio Backhoff
Universität Wien
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Talks in Financial and Insurance Mathematics

Titel The Mean Field Schrödinger Problem
Referent:in, Affiliation Prof. Dr. Julio Backhoff, Universität Wien
Datum, Zeit 22. April 2021, 17:00-18:00
Ort Zoom
Abstract In the classical Schrödinger problem, the goal is to retrieve the most likely time-evolution of a swarm of particles given observations at an initial and a terminal time. Via a large deviation argument, this problem is well approximated, as the number of particles goes to infinity, by a problem of (convex) entropy minimization under linear constraints. In this talk we discuss a natural generalization of the problem when particles are not independent anymore, but they interact through their drifts in a mean field fashion. We will first argue, via large deviations, that this problem is likewise well approximated by a problem of (non-convex) entropy minimization under linear constraints. Using stochastic control techniques, we will then explain how to characterize minimizers of the latter problem via a forward-backward system of stochastic differential equations of mean-field type. Finally we will explain how, under suitable ergodicity assumptions, it is possible to quantify that the effect at an intermediate time of the initial and terminal observations goes fast to zero as we let the time-horizon of the problem go to infinity. This talk is based on joint work with G. Conforti, I. Gentil and C. Leonard.
The Mean Field Schrödinger Problemread_more
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29. April 2021
17:00-18:00 		Dr. Sara Svaluto-Ferro
Universität Wien
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Talks in Financial and Insurance Mathematics

Titel From Signature-Based Models to Affine and Polynomial Processes and back
Referent:in, Affiliation Dr. Sara Svaluto-Ferro, Universität Wien
Datum, Zeit 29. April 2021, 17:00-18:00
Ort Zoom
Abstract Modern universal classes of dynamic processes, based on neural networks or signature methods, have recently entered the field of stochastic modeling, in particular in Mathematical Finance. This has opened the door to more data-driven and thus more robust model selection mechanisms, while principles like no arbitrage still apply. We analyze here different types of signature models. In the first part, we focus on models based on the signature of a supporting process, which can range from a Brownian motion, to a multidimensional Levy-process, to a general multidimensional tractable stochastic process, to the times series corresponding to some liquid objects on the market. We also present methods how to fit these models to data. In the second part we focus on signature SDEs, i.e. (possibly Lévy driven) SDEs whose characteristics are linear functions of the process’ signature. We show how these new models can be embedded in the framework of affine and polynomial processes, which have been - due to their tractability - the dominating process class prior to the new era of highly overparametrized dynamic models. We show that generic classes of diffusion models can be described in terms of a signature SDEs. This allows to get power series expansions for expected values of analytic functions of the process' marginals. The talk is based on joint works with Christa Cuchiero, Guido Gazzani, Francesca Primavera and Josef Teichmann.
From Signature-Based Models to Affine and Polynomial Processes and backread_more
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6. Mai 2021
17:00-18:00 		Prof. Dr. Stéphane Villeneuve
Toulouse School of Economics
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Talks in Financial and Insurance Mathematics

Titel Linear Optimal Contracts in a Gaussian World
Referent:in, Affiliation Prof. Dr. Stéphane Villeneuve, Toulouse School of Economics
Datum, Zeit 6. Mai 2021, 17:00-18:00
Ort Zoom
Abstract Since the famous paper by Holmstrom and Milgrom, it is well known that linear contracts are optimal in a world where the output process is a Brownian motion and the preferences are CARA. In this talk, I will review probabilistic techniques for solving a principal-agent problem to show how true it is. I will extend the explicit linear solution of the principal-agent model in the general framework of a Gaussian process, including for instance fractional Brownian motion. The talk is based on a current project with Eduardo Abi Jaber.
Linear Optimal Contracts in a Gaussian Worldread_more
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13. Mai 2021
17:00-18:00
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Talks in Financial and Insurance Mathematics

Titel No seminar (Ascension Day)
Referent:in, Affiliation
Datum, Zeit 13. Mai 2021, 17:00-18:00
Ort
No seminar (Ascension Day)
20. Mai 2021
17:00-18:00 		Prof. Dr. Christoph Czichowsky
London School of Economics
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Talks in Financial and Insurance Mathematics

Titel Rough Volatility and Portfolio Optimisation under Transaction Costs
Referent:in, Affiliation Prof. Dr. Christoph Czichowsky, London School of Economics
Datum, Zeit 20. Mai 2021, 17:00-18:00
Ort Zoom
Abstract Rough volatility models have become quite popular recently, as they capture both the fractional scaling of the time series of the historic volatility (Gatheral et al. 2018) and the behavior of the implied volatility surface (Fukasawa 2011, Bayer et al. 2016) remarkably well. In contrast to classical stochastic volatility models, the volatility process is neither a Markov process nor a semimartingale. Therefore, these models fall outside the scope of standard stochastic analysis and provide new mathematical challenges. In this talk, we investigate the impact of rough volatility processes on portfolio optimisation under transaction costs. The talk is based on joint work with Johannes Muhle-Karbe and Denis Schelling.
Rough Volatility and Portfolio Optimisation under Transaction Costsread_more
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27. Mai 2021
17:00-18:00 		Dr. Johannes Wiesel
Columbia University
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Talks in Financial and Insurance Mathematics

Titel Data Driven Robustness and Sensitivity Analysis
Referent:in, Affiliation Dr. Johannes Wiesel, Columbia University
Datum, Zeit 27. Mai 2021, 17:00-18:00
Ort Zoom
Abstract In this talk we consider sensitivity of a generic stochastic optimisation problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around a postulated model. We provide explicit formulae for the first order correction to both the value function and the optimiser. We further extend these results to optimisation under linear constraints. We then present applications to statistics, machine learning and mathematical finance. In particular we provide an explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least squares regression. We also propose measures to quantify robustness of neural networks to adversarial examples. In the realm of mathematical finance, we consider robustness of call option pricing and deduce a new Black-Scholes sensitivity, a non-parametric version of the so-called Vega. We also examine optimal investment problems as well as marginal utility pricing in detail. This talk is based on joint works with Samuel Drapeau, Daniel Bartl and Jan Obloj.
Data Driven Robustness and Sensitivity Analysisread_more
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3. Juni 2021
17:00-18:00 		Prof. Dr. Yan Dolinsky
Hebrew University of Jerusalem
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Talks in Financial and Insurance Mathematics

Titel Stochastic Stability for the Utility Maximization Problem
Referent:in, Affiliation Prof. Dr. Yan Dolinsky, Hebrew University of Jerusalem
Datum, Zeit 3. Juni 2021, 17:00-18:00
Ort Zoom
Abstract We study the continuity of the utility maximization problem under weak convergence. The first part deals with the frictionless case where we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. In the second part we study the continuity of the utility maximization problem in the presence of proportional transaction costs. Our main result says that the extended weak convergence of the underlying processes implies the convergence of the values of the corresponding utility maximization problems. Surprisingly, for the proportional transaction costs setup continuity holds under weaker assumptions than in the frictionless case.
Stochastic Stability for the Utility Maximization Problemread_more
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