Maria Flora (CREST, ENSAE) & Peter Tankov (CREST, ENSAE) Titre: Green investment and asset stranding under transition scenario uncertainty Abstract: We develop a real-options approach to evaluate energy assets and potential investment projects under transition scenario uncertainty. Dynamic scenario uncertainty is modelled by assuming that the economic agent acquires the information about the scenario progressively by observing a signal. The problem of valuing an investment is formulated as an American option pricing problem, where the optimal exercise time corresponds to the time of entering into a potential investment project or the time of selling a potentially stranded asset. To illustrate our approach, we apply representative scenarios from different integrated assessment models to the examples of a coal-fired power plant without Carbon Capture and Storage (CCS) and potential investment into a biomass power plant with CCS.   Download slides    

Speaker: Ahmed Kebaier (LaMME, Université d'Evry) Titre: Quantifying uncertainty with a derivative tracking SDE model and application to wind power forecast data Abstract: We develop a data-driven methodology based on parametric Itô’s Stochastic Differential Equations (SDEs) to capture the real asymmetric dynamics of forecast errors, including the uncertainty of the forecast at time zero. Our SDE framework features time-derivative tracking of the forecast, time-varying mean-reversion parameter, and an improved state-dependent diffusion term. Proofs of the existence, strong uniqueness, and boundedness of the SDE solutions are shown by imposing conditions on the time-varying mean-reversion parameter. We develop the structure of the drift term based on sound mathematical theory. A truncation procedure regularizes the prediction function to ensure that the trajectories do not reach the boundaries almost surely in a finite time. Inference based on approximate likelihood, constructed through the moment-matching technique both in the original forecast error space and in the Lamperti space, is performed through numerical optimization procedures. We propose a fixed-point likelihood optimization approach in the Lamperti space. Another novel contribution is the characterization of the uncertainty of the forecast at time zero, which turns out to be crucial in practice. We extend the model specification by considering the length of the unknown time interval preceding the first time a forecast is provided through an additional parameter in the density of the initial transition. All the procedures are agnostic of the forecasting technology, and they enable comparisons between different forecast providers. We apply our SDE framework to model historical Uruguayan normalized wind power production and forecast data between April and December 2019. Sharp empirical confidence bands of wind power production forecast error are obtained for the best-selected model.   A joint work with Renzo Caballero, Marco Scavino and Raúl Tempone. Download slides

Mohamed Balhali (Climate Economics Chair & Université Paris-Dauphine). Titre: A mean-field model for the spatial distribution of labour, housing and urban air pollution Abstract:  There exists a relationship between urban air pollution and economic activity: economic activity generates pollution, for instance through heating and transportation ; in turn, pollution spreads around and generates economic disutility. We develop a mean-field model of city coupling a labour market, a housing market, and pollution resulting from automobile commuting. Pollution is modelled through an advection-diffusion equation aiming at representing its physical dispersion.  Agents choose where to work and live in order to maximize their utility, by consuming goods, housing surface and valuing air quality. We prove existence of equilibria, and explore uniqueness when the number of job locations is finite. We provide numerical simulations and we obtain analytical results in the case of a linear monocentric city. A joint work with Quentin Petit (CEREMADE, Université Paris-Dauphine). Download slides

Title: Product Recommendations Systems and Price Competition Abstract: We study competing retailers’ choice of product recommender systems and the impact of these choices on price competition. We start by comparing two approaches to product recommendation: (i) broadcast product recommendations, a one-size-fits-all, and (ii) personalized product recommendations. We examine the role of consumer reactance in moderating firms’ approach to product recommendations. We then propose a competition-based rationale for the prevalent collaborative filtering approach to product recommendation. Download slides

Ankur A. Kulkarni (Indian Institute of Technology, Bombay)   Title: Extracting Information from a Strategic Sender   Abstract:  The COVID-19 pandemic has brought to the fore the need for segregating travellers, visitors and the general population based on answers given to standardized questionnaires. However, not all such answers can be relied upon to be truthful and therefore the design of such questionnaires for extracting true information becomes a strategic question. We introduce a setting where a receiver aims to perfectly recover a source known privately to a strategic sender by means of such questionnaires. The sender is endowed with a utility function and sends signals to the receiver with the aim of maximizing this utility. Due to the strategic nature of the sender not all the transmitted information is truthful, and signals sent by the sender are not codewords. This leads to the question: how much true information can be extracted by the receiver from such a sender? And how does it extract this information? This talk will study this question in an information-theoretic setting. We show that, in spite of the sender being strategic and the presence of noise in the channel, there is a strategy for the receiver by which it can perfectly recover an exponentially large number of source sequences. Our analysis leads to the notion of the information extraction capacity of the sender. Operationally, this capacity can be thought of as the (exponent of the) optimal length of a questionnaire to be provided to a strategic sender. We show that the information extraction capacity generalizes the Shannon capacity of a graph, and establish bounds on this capacity. We also identify cases where this capacity is equal to its theoretical maximum, and also when it is strictly less than maximum. In the latter case, we show that the capacity is sandwiched between the independence number and the Shannon capacity of a suitably defined graph. These results lead to an exact characterization of the information extraction capacity in a large number of cases. We show that in the presence of a noisy channel, the rate of information extraction achieved by the receiver is the minimum of the zero-error capacity of the channel and the information extraction capacity of the sender. Our analysis leads to insights into a novel regime of communication involving strategic agents. Time permitting, I will consider a dual model in which the receiver plays a passive role by letting the sender commit to a strategy first. Remarkably, we find that the receiver could even benefit from letting the sender take a lead.   Bio:Ankur A. Kulkarni is an Associate Professor with the Systems and Control Engineering group and the Centre for Machine Intelligence and Data Science at the Indian Institute of Technology Bombay (IITB). His research interests include information theory, game theory, stochastic control, combinatorial coding theory problems, optimization, and operations research. He received his B.Tech. from IITB in 2006, followed by M.S. in 2008 and Ph.D. in 2010, both from the University of Illinois at Urbana-Champaign (UIUC). From 2010-2012 he was a post-doctoral researcher at the Coordinated Science Laboratory at UIUC. He was an Associate (from 2015--2018) ...

Maxime Colomb (Inria-IGN), Nicolas Gilet (Inria) et Denis Talay (Inria et Ecole Polytechnique) Titre: ICI : un simulateur INRIA-IGN à l’échelle individuelle de propagation d’épidémie au sein d’une ville Résumé:  Les modèles mathématiques ont été de plus en plus utilisés pour modéliser la propagation de l'épidémie de COVID-19. Ils permettent d'adapter la prise de décision dans l'instauration de nouvelles mesures sanitaires. Toutefois, la plupart des modèles épidémiologiques (entre autres, les modèles macroscopiques SIR/SEIR) reposent sur une représentation très simplifiée des environnements urbains et de la population. Ainsi, les épidémiologistes se sont basés sur des modèles comportementaux (Leung et al, 2020) permettant de dégager les tendances globales de l'épidémie de COVID-19 sur de larges portions d'une population homogène. Bien que ces modèles aient des résultats convenables pour prévoir les tendances globales d'évolution d'une épidémie sur de larges portions de population, ils ne peuvent anticiper les évolutions locales de la contamination sur des populations hétérogènes du point de vue sanitaire, ni prédire les effets de mesures sanitaires ciblées. Comme la contamination par la COVID-19 a les aérosols comme vecteurs, la modélisation des contacts entre individus, et particulièrement en espace clos, est primordiale. Par conséquent, il est nécessaire de prendre en compte la complexité et l’hétérogénéité de l'espace géographique (surface disponible, taux de fréquentation, etc.) et des caractéristiques des individus (situation familiale, profession, âge, etc.). Les modèles correspondants sont appelés modèles individus-centrés et commencent à donner des résultats satisfaisants concernant la modélisation de l'épidémie de COVID-19 (Drogoul et al, 2021). Le projet ICI (INRIA - Collaboration - IGN) est un simulateur de propagation d’épidémie reposant sur une modélisation très détaillée d’un espace urbain et de la circulation des personnes à l’intérieur de cet espace. Il est le fruit d'une équipe pluridisciplinaire entre des chercheurs de l'INRIA, de l'École Polytechnique, du CNRS et de l'IGN. Il a pour but d'évaluer l'évolution de la propagation de l'épidémie au moyen de statistiques de contamination entre individus et d'indicateurs importants (R0, taux d'incidence) calculés à partir des états successifs des populations réalistes simulées. La réplication d'un grand nombre de ces simulations permet de dégager des tendances robustes.Le modèle ICI repose sur le couplage de deux modélisations distinctes. D'une part, l'espace géographique est modélisé d'une manière très précise à l'échelle de l'individu considéré comme appartenant à un ménage et un habitat et fréquentant des points d'intérêts et un lieu de travail. De plus, le modèle ICI intègre les caractéristiques démographiques des individus (type de ménage, sexe, âge) et leurs habitudes de déplacement (trajets domicile/travail, loisirs, etc.). D'autre part, la simulation de la propagation de l'épidémie doit s'adapter à cette échelle fine et détaillée de la population et de l'espace. En raison de la très forte hétérogénéité des caractéristiques de la COVID-19 (temps d’incubation, présence de super-contaminateurs,…), il est nécessaire de prendre en compte de multiples aléas. Une méthode de Monte Carlo consiste à simuler les déplacements quotidiens de la population synthétique en y ajoutant des probabilités liées à l'espace (probabilité de sortie, d’aller au travail,…) et des probabilités de contamination entre individus lors de leurs croisements. Pour la réalisation d'un grand nombre de simulations de transmissions de la maladie au sein de populations de très grande taille, le projet emploie des technologies de calcul haute performance (parallélisation sur des super-calculateurs).Download slides

Luciano Campi (Università degli Studi di Milano). Title : Mean field coarse correlated equilibria for linear-quadratic games with an application to emissions’ abatement   Abstract :  Coarse correlated equilibria are generalizations of Nash equilibria which have first been introduced in Moulin et Vial (1978). They include a correlation device which can be interpreted as a mediator recommending strategies to the players, which makes it particularly relevant in a context of market failure.  We develop a methodology to compute mean-field coarse correlated equilibria (CCEs) in a linear-quadratic framework. We discuss the specifications of the objective functional under which CCEs outperform Nash equilibria (NEs) in terms of both social utility and control levels. We show that the mean field limit CCEs we found allow to build approximate CCEs in N-player setting. Finally, we apply such a methodology to some relevant models, in particular to a CO2 abatement game between countries (a slightly modified version of Barrett (1994)). We show that in that model CCEs allow to reach higher abatement levels than the NE, with higher global utility.  The talk is based on a joint project with F. Cannerozzi (Milan University) and F. Cartellier (ENSAE).   Download slides