Category Reports

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 [...]

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 [...]

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 [...]

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 [...]

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 [...]

RR-FiME-12-06 Giuseppe Benedetti We analyze a principal-agent problem between the state (principal) and a firm (agent) which produces carbon emissions. In particular, the aim of the state is to motivate the firm to reduce those emissions as much as possible by structuring an appropriate incentive policy. We allow for two different kinds of incentives: a \negative" one, typically represented by a fee to pay at a given time T if emissions are too high; and a \positive" one, in the form of continuous-time Read more [...]

Stéphane Villeneuve, Xavier Warin In this paper, we develop a dynamic model that captures the interaction between a firm's cash reserves, the risk management policy and the profitability of a nonpredictable irreversible investment opportunity. We consider a firm that has assets in place generating a stochastic cash- flow stream. The firm has a non-predictable growth opportunity to expand its operation size by paying a sunk cost. When the opportunity is available, the firm can finance it either Read more [...]

RR-FiME-12-05 Stéphane GOUTTE, Nadia OUDJANE, Francesco RUSSO Given a process with independent increments X (not necessarily a martingale) and a large class of square integrable r.v. H = f(XT ), f being the Fourier transform of a finite measure μ, we provide explicit Kunita-Watanabe and Föllmer-Schweizer decompositions. The representation is expressed by means of two significant maps: the expectation and derivative operators related to the characteristics of X. We also provide an explicit expression Read more [...]

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 and hedge derivatives on produced goods. This general framework covers the interesting case of an electricity producer who wants to hedge a financial position and can trade commodities which are also inputs for his system. This extends the framework of Bouchard & Nguyen Read more [...]

RR-FiME-11-09 Pierre Del Moral, Peng Hu, Nadia Oudjane We present a new algorithm to compute the Snell envelope in the specific case where the criteria to optimize is associated with a small probability or a rare event. This new approach combines the Stochastic Mesh approach of Broadie and Glasserman with a particle approximation scheme based on a specific change of measure designed to concentrate the computational effort in regions pointed out by the criteria. The theoretical analysis of this Read more [...]