Category Rapports

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 [...]

Juin
2012

A Principal-Agent Problem for Emissions' Reduction

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 [...]

Fév
2012

On Some Expectation and Derivative Operators Related to Integral Representations of Random Variables with Respect to a PII process

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 [...]

Fév
2012

Optimal Liquidity Management and Hedging in the Presence

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 [...]

Jan
2012

A note on super-hedging for investor-producers

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 [...]

Nov
2011

Snell Envelope with Small Probability Criteria

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 [...]

Oct
2011

Testing the Nullity of Coefficients of a GARCH Model with Exogenously-Driven Volatility

RR-FiME-11-08 Nazim Regnard This paper establishes the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of a GARCH(1,1) process with time-varying cofficients driven by an exogenous variable, when some true coefficients may be null. The QMLE is shown to be consistent. Its asymptotic distribution is a projection of a normal vector distribution onto a convex cone. Furthermore, the QMLE is shown to converge to its asymptotic distribution locally uniformly. We then consider the Read more [...]

Oct
2011

Variance Optimal Hedging for Discrete Time Processes with Independent Increments. Application to Electricity Markets

RR-FiME-11-10 Stéphane GOUTTE, Nadia OUDJANE, Francesco RUSSO We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Föllmer-Schweizer decomposition for solving the mean-variance hedging problem. In particular, we establish that decomposition explicitly, for Read more [...]

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