Meetings, workshops and conferences have been cancelled worldwide: senior researcher as well as young PhD students can only interact virtually. To keep the active spirit of our whole scientific community going and to continue solving financial problems of our times, we provide virtual ways of scientific exchange for the time being.

We organise an online talk every second Thursday, alternating with the talks set up by the SIAM activity group on financial mathematics and engineering (

Find the list of the BFS One World Seminars below.


Date: Thursday, 20 May 2021

Speaker: TBA

Title: TBA

Abstract: TBA

Thursday, 20 May 2021, 19:00 (GMT +2)

Registration is free but compulsory:

Date: Thursday, 06 May 2021

Speaker: Matheus Grasselli (McMaster University)

Title: TBA

Abstract: TBA

Thursday, 06 May 2021, 19:00 (GMT +2)

Registration is free but compulsory:

Date: Thursday, 22 April 2021

Speaker: Darrell Duffie (Stanford University)

Title: Fragmenting Financial Markets

Abstract: This talk on financial market design addresses the costs (and sometimes the benefits) of fragmenting trade across multiple venues.
Size discovery trading crosses buy and sell orders, with no bid-ask spread and no price impact, by exploiting the price determined on a separate exchange market.
Although popular in practice, size discovery reduces the depth of exchange markets and, as modeled, worsens overall allocative efficiency.
On the other hand, fragmenting trade in the same asset across multiple exchanges can improve allocative efficiency.
This talk draws from research with Samuel Antill and Daniel Chen.

Thursday, 22 April 2021, 19:00 (GMT +2)

Registration is free but compulsory:

Date: Thursday, 08 April 2021

Speaker: Tomoyuki Ichiba (University of California Santa Barbara)

Title: Relative arbitrage among investors

Abstract: The relative arbitrage portfolio, formulated in Stochastic Portfolio Theory (SPT), outperforms a market portfolio over a given time-horizon with probability one under some conditions on the volatilities in the market, where the optimal relative arbitrage can be characterized by the smallest nonnegative continuous solution of a Cauchy problem. In this talk, we consider two regimes: finitely many investors and mean-field, and the corresponding Nash equilibrium of investors who compete with a benchmark determined by the market portfolio and other investors’ performance. With the market price of risk processes depending on the market portfolio and total volumes invested, we solve the multi-agent optimization problem under the framework of SPT. This is joint work with Tianjiao Yang.

Thursday, 08 April 2021, 19:00 (GMT +2)

Registration is free but compulsory:

Date: Thursday, 25 March 2021

Speaker: Bruno Bouchard (Université Paris Dauphine)

Title: Ito’s formula for concave or C1 path-dependent functions and applications in mathematical finance

Abstract: We will discuss several versions of the Ito’s formula in the case where the function is path-dependent and only concave or C1 in the sense of Dupire. In particular, we will show that it can be used to solve (super-) hedging problems in the context of market-impact or under volatility uncertainty.

Thursday, 25 March 2021, 19:00 (GMT +1)

Slides to talk:

Date: Thursday, 11 March 2021

Speaker: Tom Hurd (McMaster University)

Title: COVID-19: Modelling Another Global Systemic Phenomenon

Abstract: This talk will describe my efforts to comprehend the second great global crisis in our lifetime, based on what I learned from trying to model the Great Financial Crisis. I’ll try to convince you that insights into systemic risk made by financial mathematicians lead to network pandemic models that provide unified understanding not easy to discern from conventional SIR models. The Inhomogeneous Random Social Network (IRSN) framework, a direct offshoot of the Inhomogeneous Random Financial Network (IRFN) framework I developed in 2019, combines agent-based assumptions with a hierarchical network architecture for human society, with an aim to capture the daily dynamics of the spread of infection in a highly heterogenous population. The stochastic cascade dynamics can be simulated for networks with a moderate size N, or, under a certain convenient mathematical assumption, computed analytically in the large N limit. Since agent-based simulation experiments rapidly exceed available computer resources, I like to see what can be learned with the large N shortcut, which is comparable in computation time to conventional SIR methods. Three aspects of the framework illustrate some of the underlying mathematical ideas: the dose-response mechanism for infection, the role of superspreaders and how to capture frailty bias.

The paper introducing this model can be downloaded here:

Thursday, 11 March 2021, 19:00 (GMT +1)

Slides to talk:

Date: Thursday, 25 February 2021

Speaker: Shige Peng (Shandong University)

Title: Improving Value-at-Risk prediction under model uncertainty

Abstract: Several well-established benchmark predictors exist for the Value-at-risk (VaR), a main instrument for financial risk management.
Hybrid methods combining AR-GARCH filtering with skewed-t residuals and extreme value theory-based approach are particularly recommended.
This study introduces yet another VaR predictor, the G-VaR, following an entirely novel methodology. Inspired by the recent mathematical theory of sublinear expectation, the G-VaR is built upon the concept of model uncertainty which, in the present case, signifies that the inherent volatility of financial returns cannot be characterized by a single but infinite many statistical distributions.
By considering a worst scenario among these potential distributions, the G-VaR predictor is precisely identified.

Experiments on both the NASDAQ Composite Index and the S&P500 index demonstrate an excellent performance of the G-VaR predictor compared to most of benchmark VaR predictors. This talk is based on joint works with Shuzhen Yang and Jianfeng Yao.

Thursday, 25 February 2021, 12:00 (GMT +1) please note the different time – around lunchtime in central Europe!

Link to recorded talk:

Slides to talk:

Date: Thursday, 11 February 2021

Speaker: Alexander Schied (University of Waterloo)

Title: Robustness in risk measurement: the impact of incentives

Abstract: Statistical robustness is a desirable property for a regulatory risk measure. Previous research has stressed that Value at Risk is more robust than Expected Shortfall if both are applied to the same financial position. In reality, however, the regulatory choice of a particular risk measure imposes certain incentives, which impact the underlying position even before a particular risk measure is applied. Thus, one cannot decouple the technical properties of a risk measure from the incentives it creates. In this talk, we describe a first attempt of taking such incentives into account when assessing a risk measure’s robustness properties. To this end, we develop a general methodology which we call “robustness against optimization”. The new notion is studied for various classes of risk measures and expected utility and loss. In doing so, we arrive at conclusions, which are different from those of the previous literature and perhaps somewhat surprising. The talk is based on joint work with Paul Embrechts and Ruodu Wang.

Thursday, 11 February 2021, 19:00 (GMT +1)

Slides to talk:

Date: Thursday, 28 January 2021

Speaker: Yuri Saporito (Fundação Getúlio Vargas)

Title: PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations

Abstract: In this talk, we present a novel numerical method for Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [QF, 2019, originally published in 2009], where the functional Itô calculus was developed to deal with path-dependent financial derivatives contracts. More specifically, we generalize the Deep Galerkin Method (DGM) of Sirignano and Spiliopoulos [2018] to deal with these equations. The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE. We then analyze several numerical examples from the Financial Mathematics literature that show the capabilities of the method under very different situations.

Thursday, 28 January 2021, 19:00 (GMT +1)

Slides to talk:

Date: Thursday, 14 January 2021

Speaker: Agnes Sulem (Centre Inria de Paris)

Title: Optional pricing in a non-linear incomplete market model with default: the European and American cases

Abstract: We study option pricing in an incomplete market consisting of a risk-free asset and a risky asset driven by a Brownian motion and a compensated default martingale. We consider the case when the portfolio processes follow non-linear dynamics with a non-linear driver f.

We first study the superhedging prices and associated superhedging strategies for European options. By using a dynamic programming approach, we provide a dual formulation of the seller’s (superhedging) price involving a suitable set of equivalent probability measures, which we call f-martingale probability measures. We also establish a characterization of the seller’s price as the initial value of the minimal supersolution of a constrained Backward Stochastic Differential Equation with default.

We then study American options with irregular payoff in this market. Both points of view of  the seller and of the buyer are analyzed. We give a dual representation of the seller’s (superhedging) price in terms of the value of a non-linear mixed control/stopping problem, and provide two infinitesimal characterizations of the seller’s price process in terms of the minimal supersolution of a constrained reflected BSDE and of an optional reflected BSDE. Under some regularity assumptions on the payoff, we also prove a duality result for the buyer’s price in terms of the value of a non-linear control/stopping game problem.

The talk is based on joint works with Miryana Grigorova, University of Leeds and Marie-Claire Quenez, LPSM, Université Paris Denis Diderot.

Thursday, 14 January 2021, 19:00 (GMT +1)

Slides to talk:


Date: Thursday, 03 December 2020

Speaker: Jakša Cvitanić (Caltech)

Title: Optimal Fund Menus

Abstract: We study the optimal design of a menu of funds by a manager who is required to use linear pricing and does not observe the beliefs of investors regarding one of the risky assets. The optimal menu involves bundling of assets and can be explicitly constructed from the solution to a calculus of variations problem that optimizes over the indirect utility that each type of investor receives. We provide a complete characterization of the optimal menu and show that the need to maintain incentive compatibility leads the manager to offer funds that are inefficiently tilted towards the asset that is not subject to the information friction.

The talk is based on joint works with Julien Hugonnier.

Thursday, 03 December 2020, 19:00 (GMT +1)

Link to recorded talk:

Slides to talk:

Date: Thursday, 19 November 2020

Speaker: Xunyu Zhou (Columbia University)

Title: Entropy Regularization, Boltzmann Exploration, and Langevin Diffusions

Abstract: Many optimization models suffer from the same problem of being stuck in suboptimal traps, such as over-fitted solutions in multi-armed bandit problems and local optima in nonconvex optimization. A way out is to engage exploration to broaden the search space by randomizing the actions/controls.
We provide a theoretical foundation of the widely employed heuristic method in reinforcement learning called the Boltzmann exploration, by solving an entropy regularized, optimal stochastic relaxed control problem. We then apply the general results to the temperature control for Langevin diffusions in the context of nonconvex optimization. We derive a state-dependent, truncated exponential distribution that can be used to sample temperatures in a Langevin algorithm. Numerical experiments indicate promising performance compared with existing algorithms.

Thursday, 19 November 2020, 19:00 (GMT +1)

Link to recorded talk:

Slides to talk:

Date: Thursday, 05 November 2020

Speaker: Martin Larsson (Carnegie Mellon University)

Title: Finance and Statistics: Trading Analogies for Sequential Learning

Abstract: The goal of sequential learning is to draw inference from data that is gathered gradually through time. This is a typical situation in many applications, including finance. A sequential inference procedure is ‘anytime-valid’ if the decision to stop or continue an experiment can depend on anything that has been observed so far, without compromising statistical error guarantees. A recent approach to anytime-valid inference views a test statistic as a bet against the null hypothesis. These bets are constrained to be supermartingales – hence unprofitable – under the null, but designed to be profitable under the relevant alternative hypotheses. This perspective opens the door to tools from financial mathematics. In this talk I will discuss how notions such as supermartingale measures, log-optimality, and the optional decomposition theorem shed new light on anytime-valid sequential learning. (This talk is based on joint work with Wouter Koolen (CWI), Aaditya Ramdas (CMU) and Johannes Ruf (LSE).)

Thursday, 05 November 2020, 19:00 (GMT +1)

Date: Thursday, 22 October 2020

Speaker: Elisa Alos (Barcelona Graduate School of Economics)

Title: On the difference between volatility swaps and the ATM implied volatility

Abstract: This talk focuses on the difference between the fair strike of a volatility swap and the at-the-money implied volatility (ATMI) of a European call option. It is well known that the difference between these two quantities converges to zero as the time to maturity decreases. In this talk, we make use of a Malliavin calculus approach to derive an exact expression for this difference. This representation allows us to establish that the order of convergence is different in the correlated and uncorrelated cases, and that it depends on the behavior of the Malliavin derivative of the volatility process. In particular, we see that for volatilities driven by a fractional Brownian motion, this order depends on the corresponding Hurst parameter H. Moreover, in the case H ≥ 1/2, we develop a model-free approximation formula for the volatility swap in terms of the ATMI and its skew.

(Joint work with Kenichiro Shiraya)

Thursday, 22 October 2020, 19:00 CEST (Central European Summer Time)

Link to recorded talk:

Slides to talk:

Date: Thursday, 08 October 2020

Speaker: Damir Filipović (EPFL and Swiss Finance Institute)

Title: Machine Learning With Kernels for Portfolio Valuation and Risk Management

Abstract: We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel. We show asymptotic consistency and derive finite sample error bounds under conditions that are suitable for finance applications. Numerical experiments show good results in large dimensions for a moderate training sample size.

Thursday, 08 October 2020, 19:00 CEST (Central European Summer Time)

Slides to talk:

Date: Thursday, 24 September 2020

Speaker: Ludovic Tangpi (Princeton University)

Title: Backward propagation of chaos and large population games asymptotics

Abstract: In this talk we will present a generalization of the theory of propagation of chaos to backward (weakly) interacting diffusions. The focus will be on cases allowing for explicit convergence rates and concentration inequalities in Wasserstein distance for the empirical measures. As the main application, we derive results on the convergence of large population stochastic differential games to mean field games, both in the Markovian and the non-Markovian cases.
The talk is based on joint works with M. Laurière and Dylan Possamaï.

Thursday, 24 September 2020, 19:00 CEST (Central European Summer Time)

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Date: Thursday, 10 September 2020

Speaker: Christa Cuchiero (University of Vienna)

Title: Universality of affine and polynomial processes

Abstract: We elaborate on universal properties of affine and polynomial processes. In several recent works we could show that many models which are at first sight not recognized as affine or polynomial can nevertheless be embedded in this framework. For instance, essentially all examples of (rough) stochastic volatility models can be viewed as (infinite dimensional) affine or polynomial processes. Moreover, all well-known measure-valued diffusions such as the Fleming–Viot process, the Super–Brownian motion, and the Dawson–Watanabe superprocess are affine or polynomial. This suggests an inherent universality of these model classes. We try to make this mathematically precise by showing that generic classes of diffusion models are projections of infinite dimensional affine processes (which in this setup coincide with polynomial processes). A key ingredient to establish this result is the signature process, well known from rough paths theory.

The talk is based on joint works with Sara Svaluto-Ferro and Josef Teichmann.

Thursday, 10 September 2020, 19:00 CEST (Central European Summer Time)

Slides to talk:

Date: Thursday, 16 July 2020

Speaker: Julien Guyon (Bloomberg L.P., New York)

Title: The Joint S&P 500/VIX Smile Calibration Puzzle Solved

Abstract: Since VIX options started trading in 2006, many researchers have tried to build a model that jointly and exactly calibrates to the prices of S&P 500 (SPX) options, VIX futures and VIX options. So far the best attempts, which used parametric continuous-time jump-diffusion models on the SPX, could only produce approximate fits. In this talk we solve this longstanding puzzle using a completely different approach: a nonparametric discrete-time model. The model is cast as a dispersion-constrained martingale transport problem which is solved using the Sinkhorn algorithm. We prove by duality that the existence of such model means that the SPX and VIX markets are jointly arbitrage-free. The algorithm identifies joint SPX/VIX arbitrages should they arise. Our numerical experiments show that the algorithm performs very well in both low and high volatility environments. Finally, we briefly discuss:
(i) how our technique extends to continuous-time stochastic volatility models;
(ii) a remarkable feature of the SPX and VIX markets: the inversion of convex ordering, and how classical stochastic volatility models can reproduce it;
(iii) why, due to this inversion of convex ordering, and contrary to what has often been stated, among the continuous stochastic volatility models calibrated to the market smile, the Dupire local volatility model does not maximize the price of VIX futures.

Short bio: Julien Guyon is a senior quantitative analyst in the Quantitative Research group at Bloomberg L.P., New York. He is also an adjunct professor in the Department of Mathematics at Columbia University and at the Courant Institute of Mathematical Sciences, NYU. Before joining Bloomberg, Julien worked in the Global Markets Quantitative Research team at Société Générale in Paris for six years (2006-2012), and was an adjunct professor at Université Paris Diderot and Ecole des Ponts ParisTech. He co-authored the book Nonlinear Option Pricing (Chapman & Hall, CRC Financial Mathematics Series, 2014) with Pierre Henry-Labordère. His main research interests include nonlinear problems, volatility and correlation modeling, and numerical probabilistic methods. Julien holds a Ph.D. in Probability Theory and Statistics from Ecole des Ponts ParisTech. He graduated from Ecole Polytechnique (Paris), Université Pierre-et-Marie-Curie (Paris), and Ecole des Ponts ParisTech. A big soccer fan, Julien has also developed a strong interest in sports analytics, and has published several articles on the FIFA World Cup, the UEFA Champions League, and the UEFA Euro in top-tier newspapers such as The New York Times, The Times, Le Monde, and El Pais. Some of his suggestions for draws and competition formats have already been implemented by FIFA and UEFA.

Thursday, 16 July 2020, 19:00 CEST (Central European Summer Time)

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Date: Thursday, 02 July 2020

Speaker: Xin Guo (University of California Berkeley)

Title: Understanding GANs through MFGs and SDEs approximations

Abstract: Generative Adversarial Networks (GANs) have celebrated great empirical success, especially in image generation and processing. There is a recent surge of interest in GANs to financial applications, including asset pricing, portfolio optimization, and multi-agent market simulation.
In this talk, we will discuss some recent progress in mathematical understanding of GANs. The first is the theoretical connection between GANs and MFGs: interpreting MFGs as GANs, on one hand, allows us to devise GANs-based algorithm to solve high dimensional MFGs. Interpreting GANs as MFGs, on the other hand, provides a new and probabilistic foundation for GANs.
The second is on approximating GANs training in the form of SDEs. This SDEs approximation provides, for the first time, an analytical tool for resolving some well-recognized  issues in the machine learning community for GANs training.

Thursday, 2 July 2020, 19:00 CEST (Central European Summer Time)

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Date: Thursday, 18 June 2020

Speaker: Peter Tankov (ENSAE Paris)

Title: Environmental Impact Investing: how green-minded investors spur companies to reduce their emissions

Abstract: We develop a dynamic equilibrium model to explain how green investing spurs companies to reduce their greenhouse gas emissions by raising their cost of capital. In the model, two groups of CARA investors with different views on future environmental risks determine the cost of capital for a group of polluting companies, which then play an emission-reduction game to maximize their profits. As a result, companies’ emissions decrease when the proportion of green investors and their environmental stringency increase, as well as when the marginal abatement cost decreases. However, heightened uncertainty about future environmental risks alleviates the pressure on the cost of capital for the most carbon-intensive companies and pushes them to increase their emissions. Consistent with the nature of environmental risks, this uncertainty is modeled as non-Gaussian. We provide empirical evidence supporting our results by focusing on United States stocks and using green fund holdings between 2006 and 2018 to proxy for green investors’ beliefs. When the fraction of assets managed by green investors doubles, companies’ carbon intensity drops by 5% per year.

Joint work with Tiziano De Angelis and Olivier David Zerbib.

Thursday, 18 June 2020, 19:00 CEST (Central European Summer Time)

Link to recorded talk:

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Date: Thursday, 04 June 2020

Speaker: Nizar Touzi (Ecole Polytechnique Paris)

Title: Is there a Golden Parachute in Sannikov’s principal-agent problem?

Abstract: This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov (2008) in the extended context allowing for possible different discount factors of both parties. The agent’s problem is to seek for optimal effort, given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent’s response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirement.

A Golden parachute is a situation where the agent ceases any efforts at some positive stopping time, and receives a payment afterwards, possibly consisting of a lump sum and/or a continuous stream of payments. We show that a Golden Parachute only exists in certain specific circumstances. This is in contrast with the results claimed by Sannikov (2008) where the only requirement is a positive agent’s marginal cost of effort at zero. Namely, we show that there is no Golden Parachute if this parameter is too large. Similarly, in the context of a concave marginal utility, there is no Golden Parachute if the agent’s utility function has a too negative curvature at zero.

In the general case, we provide a rigorous analysis of this problem and we prove that an agent with positive reservation utility is either never retired by the principal, or retired above some given threshold (as in Sannikov (2008)’s solution). In particular, different discount factors induce naturally a face-lifted utility function, which allows to reduce the whole analysis to the equal-discount factors setting. Finally, we also confirm that an agent with small reservation utility does have an informational rent, meaning that the principal optimally offers him a contract with strictly higher utility value.

Thursday, 4 June 2020, 19:00 CEST (Central European Summer Time)

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Date: Thursday, 21 May 2020

Speaker: Jan Obloj (University of Oxford)

Title: Data driven robustness and uncertainty sensitivity analysis

Abstract: In this talk, I will showcase how methods from optimal transport and distributionally robust optimisation allow to capture and quantify sensitivity to model uncertainty for a myriad of problems.
We consider a generic stochastic optimisation problem. This could be a mean-variance or a utility maximisation portfolio allocation problem, an optimised certainty equivalent or a risk measure computation, a standard regression or a deep learning problem. At the heart of the optimisation is a probability measure, or a model, which describes the system. It could come from data, simulation or a modelling effort but there is always a degree of uncertainty about it.
We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated measure. Our main results provide explicit formulae for the first order correction to both the value function and the optimiser. We further extend our results to optimisation under linear constraints. Our sensitivity analysis of the distributionally robust optimisation problems finds applications in statistics, machine learning, mathematical finance and uncertainty quantification.
In the talk, I will discuss several financial examples anchored in a one-step financial model and compute their sensitivity to model uncertainty. These will include: option pricing, mean-variance portfolio selection, optimised certainty equivalent and similar risk assessments as well as a robust version of Davis’ marginal utility option pricing. I will also discuss briefly other applications, such as explicit formulae for first-order approximations of square-root LASSO and square-root Ridge optimisers and measures of NN architecture robustness wrt to adversarial data. I will also showcase the link with building data-driven estimators of risk measures.
Talk based on joint works with Daniel Bartl, Samuel Drapeau and Johannes Wiesel.

Thursday, 21 May 2020, 19:00 CEST (Central European Summer Time)

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Date: Thursday, 07 May 2020

Speaker: Paul Embrechts (Professor emeritus ETH Zurich)

Title: Operational Risk revisited: from Basel to the coronavirus

Abstract: In the company of market and credit risk, from a more mathematical point of view, operational risk has always been viewed as the “little brother or sister”. And yet as the 2007-2009 Financial Crisis has shown and as we no doubt will find out from the coronavirus crisis sometime in the future, operational risk is an eminently important, and surely technically demanding risk category within the regulatory frameworks of insurance (Solvency 2, say) and banking (the various Basel frameworks). In this talk I will sketch some of its history, some of the main technical modeling tools used and comment on methodological ways forward. I will also discuss some of the early lessons (hopefully) learned from the current coronavirus pandemic.

Thursday, 7 May 2020, 19:00 CEST (Central European Summer Time)

Link to recorded talk:

Slides to talk:

Date: Thursday, 23 April 2020

Speaker: Mathieu Rosenbaum (Ecole Polytechnique, Paris)

Title: Super-Heston rough volatility, Zumbach effect and the Guyon’s conjecture

Abstract: The rough Heston model is known to reproduce accurately the behavior of historical volatility time series as well as the dynamics of the implied volatility surface. However, some argue that actual volatility tails are even fatter than that generated in the rough Heston model. Furthermore, it fails to reproduce a very subtle property of historical data referred to as Zumbach effect. In this talk we address these two concerns introducing so-called super-Heston rough volatility models. It turns out that these models enable us to obtain joint calibration of both SPX and VIX implied volatility surfaces, hence providing a counter-example to a long-standing conjecture by Julien Guyon (this is joint work with Aditi Dandapani, Jim Gatheral and Paul Jusselin).

Thursday, 23 April 2020, 19:00 CEST (Central European Summer Time)