Dylan Possamaï

Dylan Possamaï
ETH Zurich | ETH Zürich · Department of Mathematics

PhD

About

76
Publications
10,647
Reads
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1,048
Citations
Additional affiliations
August 2020 - present
ETH Zurich
Position
  • Professor (Full)
September 2017 - July 2020
Columbia University
Position
  • Professor (Assistant)
September 2015 - August 2016
École Polytechnique
Position
  • Professeur Chargé de Cours
Education
October 2009 - December 2011
École Polytechnique
Field of study
  • Financial Mathematics
September 2008 - August 2009
Sorbonne Université
Field of study
  • Financial Mathematics
September 2005 - August 2008
École Polytechnique
Field of study
  • Applied mathematics

Publications

Publications (76)
Article
Full-text available
Motivated by the recent studies on the green bond market, we build a Principal–Agent model in which an investor trades on a portfolio of green and conventional bonds, both issued by the same governmental entity. The government provides incentives to the bondholder in order to increase the amount invested in green bonds. These incentives are, optima...
Article
Full-text available
In this work, we provide a general mathematical formalism to study the optimal control of an epidemic, such as the COVID-19 pandemic, via incentives to lockdown and testing. In particular, we model the interplay between the government and the population as a principal–agent problem with moral hazard, à la Cvitanić et al. (Finance Stoch 22(1):1–37,...
Preprint
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We design a market-making model \`a la Avellaneda-Stoikov in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers' behaviour, modelled through a mean-field interaction. We derive, up to the resoluti...
Article
Full-text available
Demand response programs in retail electricity markets are very popular. However, despite their success in reducing average consumption, the random responsiveness of consumers to price events makes their efficiency questionable to achieve the flexibility needed for electric systems with a large share of renewable energy. This paper aims at designin...
Article
Full-text available
We study a McKean–Vlasov optimal control problem with common noise in order to establish the corresponding limit theory as well as the equivalence between different formulations, including strong, weak, and relaxed formulations. In contrast to the strong formulation, in which the problem is formulated on a fixed probability space equipped with two...
Preprint
Full-text available
In this paper we study a pollution regulation problem in an electricity market with a network structure. The market is ruled by an independent system operator (ISO for short) who has the goal of reducing the pollutant emissions of the providers in the network, by encouraging the use of cleaner technologies. The problem of the ISO formulates as a co...
Preprint
Full-text available
In this paper, we obtain stability results for backward stochastic differential equations with jumps (BSDEs) in a very general framework. More specifically, we consider a convergent sequence of standard data, each associated to their own filtration, and we prove that the associated sequence of (unique) solutions is also convergent. The current resu...
Preprint
Full-text available
This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by \citeauthor*{carmona2015probabilistic} \cite{carmona2015probabilistic}, we consider a fully non-Markovian setting allowing for drift control, and interactions through the joint distribution of players' states and...
Article
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We study risk-sharing economies where heterogeneous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully coupled forward–backward stochastic differential equations. We show that a unique solution exists provided that the agents’ prefe...
Preprint
Full-text available
Motivated by the recent studies on the green bond market, we build a model in which an investor trades on a portfolio of green and conventional bonds, both issued by the same governmental entity. The government provides incentives to the bondholder in order to increase the amount invested in green bonds. These incentives are, optimally, indexed on...
Article
Full-text available
We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a continuum of consumers with mean–field interaction, whose consumption is impacted by a common noise. We formulate the problem as a Principal–Agent problem with moral hazard in which the Principal—she—is an electricity producer who obs...
Preprint
Full-text available
We consider the control of the COVID-19 pandemic via incentives, through either stochastic SIS or SIR compartmental models. When the epidemic is ongoing, the population can reduce interactions between individuals in order to decrease the rate of transmission of the disease, and thus limit the epidemic. However, this effort comes at a cost for the p...
Preprint
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We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite dimensional system of standard backward SDEs and establish its well-posedness, and we show that it is equivalent to that of a type-I backward stochastic Volterra integral equation. We also establish a...
Preprint
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This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov, in the extended context allowing for possibly different discount rates 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 opt...
Article
Full-text available
We consider zero-sum stochastic differential games with possibly path-dependent controlled state. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback type. Under some restrictions, needed for the a priori regularity of the upper and lower value functions of th...
Article
Full-text available
In this paper, we extend the optimal securitization model of Pag\`es [41] and Possama\"i and Pag\`es [42] between an investor and a bank to a setting allowing both moral hazard and adverse selection. Following the recent approach to these problems of Cvitani\'c, Wan and Yang [12], we characterize explicitly and rigorously the so-called credible set...
Preprint
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We develop a theory for continuous-time non-Markovian stochastic control problems which are inherently time-inconsistent. Their distinguishing feature is that the classical Bellman optimality principle no longer holds. Our formulation is cast within the framework of a controlled non-Markovian forward stochastic differential equation, and a general...
Preprint
Full-text available
We study a McKean-Vlasov optimal control problem with common noise, in order to establish the corresponding limit theory, as well as the equivalence between different formulations, including the strong, weak and relaxed formulation. In contrast to the strong formulation, where the problem is formulated on a fixed probability space equipped with two...
Preprint
Full-text available
Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimise their quotes in a Nash equilibrium fashion, providing best r...
Preprint
Full-text available
We study the McKean-Vlasov optimal control problem with common noise in various formulations, namely the strong and weak formulation, as well as the Markovian and non-Markovian formulations, and allowing for the law of the control process to appear in the state dynamics. By interpreting the controls as probability measures on an appropriate canonic...
Article
Full-text available
In this article, we propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate the links between our 2BDSDEs and a class of parabolic Fully nonLinear Stochastic PDes. Pre...
Article
Full-text available
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales, each adapted to its own filtration, and a sequence of random variables measurable with respect to those filtrations. We assume that the terminal values of the martingales and the associated...
Preprint
Full-text available
We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a mean-field of consumers, whose consumption is impacted by a common noise. We formulate the problem as a Principal-Agent problem with moral hazard in which the Principal - she - is an electricity producer who observes continuously the...
Preprint
Full-text available
We study a risk-sharing equilibrium where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic differential equations. We show that a unique solution generally exists provided that the...
Article
Full-text available
We study a risk-sharing equilibrium where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic differential equations. We show that a unique solution generally exists provided that the...
Article
Full-text available
In this paper, we extend the Holmstr\"{o}m and Milgrom problem [30] by adding uncertainty about the volatility of the output for both the agent and the principal. We study more precisely the impact of the "Nature" playing against the Agent and the Principal by choosing the worst possible volatility of the output. We solve the first-best and the sec...
Preprint
Full-text available
Despite the success of demand response programs in retail electricity markets in reducing average consumption, the literature shows failure to reduce the variance of consumers' responses. This paper aims at designing demand response contracts which allow to act on both the average consumption and its variance. The interaction between the producer a...
Preprint
Full-text available
We consider zero-sum stochastic differential games with possibly path-dependent controlled state. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback type. Under some restrictions, needed for the a priori regularity of the upper and lower value functions of th...
Preprint
Full-text available
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables measurable with respect to those filtrations. We assume that the terminal values of the martingales and the associated...
Article
Full-text available
We consider a general formulation of the Principal-Agent problem from Contract Theory, on a finite horizon. We show how to reduce the problem to a stochastic control problem which may be analyzed by the standard tools of control theory. In particular, Agent's value function appears naturally as a controlled state variable for the Principal's proble...
Article
Full-text available
Despite the success of demand response programs in retail electricity markets in reducing average consumption, the literature shows failure to reduce the variance of consumers' responses. This paper aims at designing demand response contracts which allow to act on both the average consumption and its variance. The interaction between the producer a...
Article
Full-text available
The aim of this short note is to fill in a gap in our earlier paper [7] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [6]. We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [5, 13] in the so-called $G-$framework.
Article
Full-text available
We study the optimal design of electricity contracts among a population of consumers with different needs. This question is tackled within the framework of Principal-Agent problem in presence of adverse selection. The particular features of electricity induce an unusual structure on the production cost, with no decreasing return to scale. We are ne...
Article
Full-text available
This paper studies a class of non-Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a Z-constrained BSDE, with dynamics associated to a non singular underlying forward process. Due to the non-Markovian environment...
Article
Full-text available
In this paper, we investigate a moral hazard problem in finite time with lump-sum and continuous payments, involving infinitely many Agents, with mean field type interactions, hired by one Principal. By reinterpreting the mean-field game faced by each Agent in terms of a mean field FBSDE, we are able to rewrite the Principal's problem as a control...
Article
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We provide a unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, which may not be quasi left-continuous. As an example of application, we prove that reflected BSDEs are well-posed in a general framework.
Article
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This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, i.e. the filtration may be stochastically discontinuous. We show that for stochastic Lipschitz generators and unbounded, pos...
Article
Full-text available
In a framework close to the one developed by Holmstr\"om and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, as well as impact (positively or negatively) the projects of the other Agents. Considering eco...
Article
Full-text available
In this paper, we study the existence of densities (with respect to the Lebesgue measure) for marginal laws of the solution (Y,Z) to a quadratic growth BSDE. Using the (by now) well-established connection between these equations and their associated semi-linear PDEs, together with the Nourdin-Viens formula, we provide estimates on these densities.
Article
Full-text available
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimization, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are non-linear generalizations of the traditional (linear) expecta...
Article
Full-text available
We provide a unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, which may not be quasi left-continuous. Unlike the previous related approaches in simpler settings, our results do not only rely on a simple application of Itô's formula and classical estimates, but use crucially appropriate generalizations of de...
Article
Full-text available
In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z, u). From a technical point of view, we use a direct fixed point approach as in Tevzadze [38], which allows us to obtain existence and uniqueness of a solution when the t...
Article
Full-text available
We provide a general Doob-Meyer decomposition for $g$-supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical supermartingales, as well as Peng's (1999) version for right-continuous $g$-supermartingales. As examples of application,...
Article
Full-text available
In this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by nu...
Article
In this paper, we provide a strong formulation of the stochastic G{\^a}teaux differentiability in order to study the sharpness of a new characterization, introduced in [6], of the Malliavin-Sobolev spaces. We also give a new internal structure of these spaces in the sense of sets inclusion.
Article
Full-text available
The aim of this paper is twofold. First, we extend the results of Matoussi et al. (2012) concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar to the ones in Crépey and Matoussi (2008), and when the two barriers are completely separate...
Article
Full-text available
We consider a contracting problem in which a principal hires an agent to manage a risky project. When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This leads to moral hazard with re...
Article
Full-text available
In this paper we provide new conditions for the Malliavin differentiability of solutions of Lipschitz or quadratic BSDEs. Our results rely on the interpretation of the Malliavin derivative as a G\^ateaux derivative in the directions of the Cameron-Martin space. Incidentally, we provide a new formulation for the characterization of the Malliavin-Sob...
Article
Full-text available
In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of their properties. We obtain in pa...
Article
Full-text available
In this paper, we study the existence of densities (with respect to the Lebesgue measure) for marginal laws of the solution $(Y,Z)$ to a quadratic growth BSDE. Using the (by now) well-established connection between these equations and their associated semi-linear PDEs, together with the Nourdin-Viens formula, we provide estimates on these densities...
Article
Full-text available
We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time T, we obtain an asymptotic expansion of the utility indifference price as a function of the asymptotic expansions of the utility maximization problems...
Article
Full-text available
We study the weak approximation of the second order Backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both robustness properties of BSDEs, as proved in Briand, Delyon and M\'emin [7], and tightness of solutions to discrete tim...
Article
Full-text available
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is nondominated. We propose studying this problem in the framework of seco...
Article
Full-text available
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context suitable for martingale optimal transportation or, more generally, for optimal transportation under controlled s...
Article
Full-text available
In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in our accompanying paper [42], the asymptotic expansion is expressed in terms of a singular ergodic control prob...
Article
Full-text available
The aim of this paper is twofold. First, we extend the results of [32] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of upper obstacles. Then, under some regularity assumptions on one of the barriers, similar to the ones in [9], and when the two barriers are completely separated, we provide a complete wellpose...
Article
Full-text available
We prove the existence of bounded solutions of quadratic backward SDEs with jumps, using a direct fixed point approach as in Tevzadze [36]. Under an additional standard assumption, we prove a uniqueness result, thanks to a comparison theorem. Then we study the properties of the corresponding $g$-expectations, we obtain in particular a non linear Do...
Article
Full-text available
We consider a financial market with liquidity cost as in \c{C}etin, Jarrow and Protter [2004], where the supply function S{\epsilon}(s,{\nu}) depends on a parameter {\epsilon}\geq0 with S0(s,{\nu})=s corresponding to the perfect liquid situation. Using the PDE characterization of \c{C}etin, Soner and Touzi [2010], of the super-hedging cost of an op...
Article
Full-text available
In this paper, we define a notion of second order backward stochastic differential equation with jumps (2BSDEJs for short), which generalizes the continuous case considered by Soner, Touzi and Zhang [33]. However, on the contrary to their formulation, where they can define pathwise the density of quadratic variation of the canonical process, in our...
Article
Full-text available
In this paper, we follow the study of second order BSDEs with jumps started in our accompanying paper [17]. We prove existence of these equations by a direct method, thus providing complete wellposedness for second order BSDEs. These equations are the natural candidates for the probabilistic interpretation of fully non-linear partial integro-differ...
Article
Full-text available
In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [9]. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are natural candidates for the probabilistic interpretation of some fully non-linear partial integ...
Article
Full-text available
In this paper, we define a notion of second order backward stochastic differential equation with jumps, which generalizes the continuous case considered by Soner, Touzi and Zhang [37]. In order to correctly define these notions, we first have to solve an important issue corresponding to the possibility to aggregate, in the sense of [39] and [10], b...
Article
Full-text available
In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in \cite{pages}, with optimal contracting between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian contagion. We provide here a comprehensive mathematical formulation of the model and show using marting...
Article
Full-text available
In this article, we build upon the work of Soner, Touzi and Zhang [35] to define a notion of a second order backward stochastic differential equation reflected on a lower cadlag obstacle. We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate some links between our reflected 2BSDEs a...
Article
Full-text available
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models (probability measures) considered here is non-dominated. We propose studying this problem in the framework of sec...
Article
Full-text available
In a recent paper, Soner, Touzi and Zhang [20] have introduced a notion of second order backward stochastic differential equations (2BSDEs for short), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in the variables $y$ and $z$. The aim of this paper i...
Article
Full-text available
We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$ variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic co...
Thesis
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This PhD dissertation presents two independent research topics dealing with contemporary issues in mathematical finance, the second one being divided into into two distinct problems. Throughout the first part of the dissertation, we study the notion of second order backward stochastic differential equations (2BSDE in the following), first introduce...
Thesis
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Cette thèse présente deux principaux sujets de recherche indépendants, le dernier étantdécliné sous la forme de deux problèmes distincts. Dans toute la première partie de la thèse, nous nous intéressons à la notion d’équations différentielles stochastiques rétrogrades du second ordre (dans la suite 2EDSR), introduite tout d’abordpar Cheridito, Sone...
Article
Full-text available
Stochastic volatility models have replaced Black-Scholes model since they are able to generate a volatility smile. However, standard models fail to capture the smile slope and level movements. The Double-Heston model provides a more flexible approach to model the stochastic variance. In this paper, we focus on numerical implementation of this model...
Article
Full-text available
Using probability change techniques introduced by Drimus for Heston model, we derive a n-th order expansion formula of Wishart option price in terms of Black-Scholes price and Black-Scholes Greeks. Numerical results are given for the second order case. Thanks to this new approximation, the smile implied by Wishart model can be better understood. Th...
Article
Full-text available
In financial mathematics, Wishart processes have emerged as an efficient tool to model stochastic covariance structures. Their numerical simulation may be quite challenging since they involve matrix processes. In this article, we propose an extensive study of financial applications of Wishart processes. First, we derive closed-form formulas for opt...

Projects

Projects (7)
Project
This project regroups some works on principal-agent problems with application to energy sector.
Project