# Category Archives: Working Papers

## A simple equilibrium model for a commodity market with spot trades and futures contracts

by Ivar Ekeland, Delphine Lautier & Bertrand Villeneuve We propose a simple model which offers a unified theoretical framework for the analysis of price and quantity relationships in commodity markets. We study the simultaneous equilibrium in the physical and futures … Continue reading

## Optimal selling rules for monetary invariant criteria: tracking the maximum of a portfolio with negative drift

by Romuald ELIE & Gilles-Edouard ESPINOSA Considering a positive portfolio diffusion X with negative drift, we investigate optimal stopping problems of the form (…) This paper unifies optimal selling rules observed by [5] for quadratic absolute distance criteria with bang-bang … Continue reading

## Exact replication under Delta constraints

by Jean-François Chassagneux, Romuald Elie & Idris Kharroubi This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim … Continue reading

## Economic growth and sustainable development: how should we discount the future?

by Qinglong Zhou, Ivar Ekeland, Yiming Long In 1987, the Brundtland Commission famously defined sustainable development as “developmentthat meets the needs of the present without compromising the needs of the future”. This paper is concerned with translating this definition in the … Continue reading

## The Flood Issue: Uniform Insurance and Collective Prevention with Risk Externalities

by Céline Grislain-Letrémy & Sabine Lemoyne de Forges Prevention policies against flood, such as dams or levees, are commonly designed by local jurisdictions and for most they exert externalities on neighboring jurisdictions. Each jurisdiction chooses its collective prevention effort depending … Continue reading

## Systemic Risk in Energy Derivative Markets: A Graph-Theory Analysis

. by Delphine Lautier & Franck Raynaud This article uses graph theory to provide novel evidence regarding market integration, a favorable condition for systemic risk tio appear in. Relying on daily futures returns covering a 12-year period, we examine cross- … Continue reading

## Risk-Parameter Estimation in Volatility Models

. by Christian Franck & Jean-Michel Zakoïan This paper introduces the concept of risk parameter in conditional volatility models of the form ǫt = σt(θ0)ηt and develops statistical procedures to estimate this parameter. For a given risk measure r, the risk parameter is expressed … Continue reading

## Ecological intuition versus Economic “reason”

by Olivier Guéant, Roger Guesnerie & Jean-Michel Lasry This article discusses the discount rate to be used in projects that aimed at preserving the environment. The model has two di§erent goods, one is the usual consumption good whose production may … Continue reading

## A note on super-hedging for investor-producers

by Adrien Nguyen Huu We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price … Continue reading

## Natural and Industrial Disasters: Land Use and Insurance

by Céline Grislain-Letrémy & Bertrand Villeneuve Uncontrolled urbanization in exposed areas increases the cost of natural and industrial disas- ters. In the case of industrial risks, these land use externalities are directly exerted on the firm which is liable for … Continue reading

## Optimal Portfolio Liquidation with Limit Orders

by Olivier Guéant, Charles-Albert Lehalle & Joaquin Fernandez Tapia This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or … Continue reading

## Dealing with the Inventory Risk

by Olivier Guéant, Charles-Albert Lehalle & Joaquin Fernandez Tapia Market makers have to continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask … Continue reading

## 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