Category Rapports

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 [...]

Mar
2011

Gas storage hedging

RR-FiME-11-04 Xavier WARIN Gaz storage valuation has been an intense subject of research during the recent years. This problem is related to optimal control problems [17], [15] and more precisely to the class of optimal switching problem. On the energy market, the gaz storage management can be seen as a so called swing option [12] with some operational contraints : each day the manager of the gas storage has to decide either to inject gaz in the storage, buying it on the gas market, either to withdraw Read more [...]

Fév
2011

A Finite Dimensional Approximation for Pricing Moving Average Options

<h3><strong><span style="color: #005d63;">M. Bernhart, P. Tankov, X. Warin</span></strong></h3> We propose a method for pricing American options whose pay-o depends on the moving average of the underlying asset price. The method uses a nite dimensional approximation of the in nite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a finite-dimensional optimal stopping problem, which we Read more [...]

Fév
2011

Swing Options Valuation: a BSDE with Constrained Jumps Approach

M. Bernhart, H. Pham, P. Tankov, X. Warin We introduce a new of probabilistic method for solving a class of impulse control problems based on their representation as Backward Stochastic Differential Equations (BDSE) with constrained jumps. As an example, our method is used to price swing options. We deal with the jump contraints by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method with Read more [...]

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