# Category Archives: Working Papers

## From infinity to one: the reduction of some MFGs to planning problems

by Olivier Guéant This paper presents recent results from Mean Field Game theory underlying the intro- duction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games … Continue reading

## Stochastic Target Problems with Controlled Loss in Jump Diffusion Models

By Ludovic Moreau Stochastic Target Problems with Controlled Loss in Jump Diffusion Models In this paper, we consider a mixed diffusion version of the stochastic target problem introduced in [3]. This consists in finding the minimum initial value of a … Continue reading

## On a mean field game approach modeling congestion and aversion in pedestrian crowds

By Aimé Lachapelle & Marie-Therese Wolfram (Cahier de la Chaire n°40) In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach … Continue reading

## A class of DCC asymmetric GARCH models driven by exogenous variables

By Jean-Michel Zakoïan (Cahier de la Chaire n°39) This paper considers Dynamic Conditional Correlations (DCC) GARCH models in which the time-varying coefficients, including the conditional correlation matrix, are functions of the realizations of an exogenous stochastic process. Time series generated … Continue reading

## A structural risk-neutral model for pricing and hedging power derivatives

By René Aïd, Luciano Campi & Nicolas Langrené (Cahier de la Chaire n°38) We develop a structural risk-neutral model for energy market modifying along several directions the approach introduced in [Aïd et al., 2009]. In particular a scarcity function is … Continue reading

## Statistical properties of derivatives: a journey in term structures

By Delphine Lautier & Franck Raynaud (Cahier de la Chaire n°37) This article presents an empirical study of thirteen derivative markets for commodity and financial assets. This paper goes beyond statistical analysis by including the maturity as a variable for … Continue reading

## Detecting the Maximum of a Mean-Reverting Scalar Diffusion

By Gilles-Edouard Espinosa & Nizar Touzi (Cahier de la Chaire n°36) Let X be a mean reverting scalar process, X the corresponding running maximum, T0 the first time X hits the level zero and ` a loss function, mainly increasing and … Continue reading

## Large liquidity expansion of super-hedging costs

By Dylan Possamai, H. Mete Soner & Nizar Touzi (Cahier de la Chaire n°35) We consider a financial market with liquidity cost as in Cetin, Jarrow and Protter (2004) where the supply function depends on a parameter with corresponding to … Continue reading

## Wellposedness of Second Order Backward SDEs

By H. Mete Soner, Nizar Touzi & Jianfeng Zhang (Cahier de la Chaire n°34) We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear … Continue reading

## Weak Dynamic Programming Principle for Viscosity Solutions

By Bruno Bouchard & Nizar Touzi (Cahier de la Chaire n°33) We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the measurable selection argument. In … Continue reading

## A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs

By Arash Fahim, Nizar Touzi & Xavier Warin (Cahier de la Chaire n°32) We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in Cheridito et al (2007), and show that it can be introduced naturally as a combination of … Continue reading

## Familiarity Breeds Institutional Investment: Evidence from US Defined Benefit Pension Plans

by Christina Atanasova & Gilles Chemla (Cahier de la Chaire n°31) This paper provides new evidence that familiarity bias affects the portfolios ofinstitutional investors. Using a sample of large US defined-benefit pension plans for the period1992 to 2002, we show … Continue reading

## On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights

By D. Crisan, K. Manolarakis & N. Touzi (Cahier de la Chaire n°30) We propose a generic framework for the analysis of Monte Carlo simulation schemes of backward SDEs. The general results are used to re-visit the convergence of the … Continue reading

## Stochastic Target Problems with Controlled Loss

By Bruno Bouchard, Romuald Elie & Nizar Touzi (Cahier de la Chaire n°29) We consider the problem of finding the minimal initial data of a controlled process which guarantees to reach a controlled target with a given probability of success or, … Continue reading

## Privately Optimal Securitization and Publicly Suboptimal Risk Sharing

By Gilles Chemla & Christopher A. Hennessy (Cahier de la Chaire n°28) Privately informed owners securitizing assets signal positive information by retaining sufficient interest. Signaling provides social bene fits, allowing uninformed investors to insure without fearing adverse selection. Instead of signaling, owners … Continue reading

## Discounting the Future: The Case of Climate Change

By Ivar Ekeland (Cahier de la Chaire n°27) According to the Stern Report on climate change, the course of the next fifty years is set: present policies will impact only in the very long term, fifty to two hundred years … Continue reading

## Strategic Capacity Investment under Holdup Threats: The Role of Contract Length and Width

by Laure Durand-Viel & Bertrand Villeneuve (Cahier de la Chaire n°26) This article analyzes the impact of incomplete contracts’ length on investment in a bilateral relationship. The seller has the power to set the contract terms whereas the buyer decides … Continue reading

## A conditionally heteroskedastic model with time-varying coefficients for daily gas spot prices

by Nazim Regnard and Jean-Michel Zakoïan (Cahier de la Chaire n°25) A novel GARCH(1,1) model, with coefficients function of the realizations of an exogenous process, is considered for the volatility of daily gas prices. A distinctive feature of the model … Continue reading

## A structural risk-neutral model of electricity

by René Aïd, Luciano Campi, Adrien Nguyen Huu and Nizar Touzi (Cahier de la Chaire n°24) The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying … Continue reading

## The Precautionary Principle and the Evaluation of Environmental Policies

by Olivier Guéant (Cahier de la Chaire n°23) This general readership article proposes an approach to evaluate what an economically and socially acceptable cost can be in the context of policies that aim at improving the environment. We stress the … Continue reading