Category Rapports

Mai
2014

Explicit Investment Rules with Time-to-build and Uncertainty

RR-FiME-14-02 René Aid, Salvatore Federico, Huyên Pham, Bertrand Villeneuve We establish explicit socially optimal rules for an irreversible investment decision with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpretations for three models of demand (arithmetic Brownian, geometric Brownian, and the Cox-Ingersoll-Ross). Committed capacity, that is, the installed capacity plus the investment in Read more [...]

Avr
2014

Hedging Expected Losses on Derivatives in Electricity Futures Markets

RR-FiME-14-01 Adrien Nguyen Huu, Nadia Oudjane  

Sep
2013

A Simple Equilibrium Model for a Commodity Market with Spot and Futures Trades

RR-FiME-13-05 Ivar Ekeland, Delphine Lautier, Bertrand Villeneuve We propose a simple equilibrium model, where the physical and the derivative markets of the commodity interact. There are three types of agents: industrial processors, inventory holders and speculators. Only the two first of them operate in the physical market. All of them, however, may initiate a position in the paper market, for hedging and/or speculation purposes. We give the necessary and sufficient conditions on the fundamentals Read more [...]

Sep
2013

Two Algorithms for the Discrete Time Approximation of Markovian Backward Stochastic Differential Equations under Local Conditions

RR-FiME-13-04 Plamen Turkedjiev Two discretizations of a novel class of Markovian backward stochastic differential equations (BSDEs) are studied. The first is the classical Euler scheme which approximates a projection of the processes Z, and the second a novel scheme based on Malliavin weights which approximates the mariginals of the process Z directly. Extending the representation theorem of Ma and Zhang [MZ02] leads to advanced a priori estimates and stability results for this class of BSDEs. Read more [...]

Juil
2013

Utility Indifference Valuation for Non-Smooth Payoffs with an Application to Power Derivatives

RR-FiME-13-03 Giuseppe Benedetti, Luciano Campi We consider the problem of exponential utility indifference valuation under the simplified framework where traded and nontraded assets are uncorrelated but where the claim to be priced possibly depends on both. Traded asset prices follow a multivariate Black and Scholes model, while nontraded asset prices evolve as generalized Ornstein-Uhlenbeck processes. We provide a BSDE characterization of the utility indifference price (UIP) for a large class Read more [...]

Mai
2013

Real option game with a random regulator: the value of being preferred

RR-FiME-13-02 Adrien Nguyen Huu We attempt to formalize a randomization procedure undertaken in pre-emptive real option games without simultaneous investment. This allows to propose a unified treatment of both real option games with and without simultaneous investment. This is done by introducing a random arbitrator with different parametrization. We then extend the study to an unfair arbitrator. This leads to competitive advantages in various asymmetrical situations. Relying on the results of Read more [...]

Jan
2013

Banking and Backloading Emission Permits

RR-FIME-13-01 Corinne CHATON, Anna CRETI, Benoît PELUCHON In this article we focus on carbon price dynamics, more specfically the impact of a policy envisaged by the European Commission to increase the CO2 price. This policy consists of removing a share of the allowances al- located for a period in order to reallocate some or all of them during the following period. To analyze the impact of this backloading we determine the CO2 market equilibrium with and without the policy, considering not only Read more [...]

Oct
2012

A Probabilistic Numerical Method for Optimal Multiple Switching Problem and Application to Investments in Electricity Generation

RR-FiME-12-07 René Aïd, Luciano Campi, Nicolas Langrené, Huyên Pham In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the size of the local hypercubes involved in the regressions, and of the truncating time horizon. Read more [...]

Août
2012

A review of optimal decision rule for investment in electricity generation

RR-FiME-12-04 Carmine De Franco, Peter Tankov, Xavier Warin We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem can be related to a triangular system of parabolic partial integro-differential equations (PIDE), which can be shown to possess unique smooth solutions in our setting. The first equation is non-linear, Read more [...]

Juil
2012

A review of optimal decision rule for investment in electricity generation

R. Aïd This paper provides an introduction to optimal investment rules in electricity generation. It attempts to bring together methods commonly used in practice to assess electricity generation investments as well as the sophisticated tools developed by mathematical economists in the last thirty years. It begins with a description of the fundamentals of the problem (economic context of the energy and electricity sectors, the technical constraints and cost structures of generation technologies). Read more [...]

Page 4 of 8