Determining the implied volatility in the Dupire equation for vanilla European call options

The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a collection of quoted option prices with different strikes

Stable Allocation Mechanism

The stable allocation problem is the generalization of the well-known and much studied stable (0,1)-matching problems to the allocation of real numbers (hours or quantities). There are two distinct sets of agents, a set I of "employees" or "buyers" and a set J of "employers" or "sellers", each agent with preferences over the opposite set and each with a given available time or quantity. In common with its specializations, and allocation problem may have exponentially many stable solutions (though in the "generic" case it has exactly one stable allocation). A mechanism is a function that selects exactly one stable allocation for any problem. The "employee-optimal" mechanism XI that always selects xI, the "employee-optimal" stable allocation, is characterized as the unique one that is, for employees, either "efficient", or "monotone", or "strategy-proof."Le problème d'allocations stables généralise les problèmes d'affectations stables (" one-to-one ", " one-to-many " ou " many-to-many ") à l'attribution de quantités réelles ou d'heures. Il existe deux ensembles d'agents distincts, un ensemble I " employés " et un ensemble J " employeurs " où chaque agent a un ordre de préférences sur les agents de l'ensemble opposé et chacun a un certain nombre d'heures. Comme dans les cas spécifiques, le problème d'allocations stables peut contenir un nombre exponentiel de stables (quoique dans le cas " générique " il admet exactement une allocation stable). Un mécanisme est une fonction qui sélectionne exactement une allocation stable pour n'importe quel problème. Le mécanisme " optimal-employés " qui sélectionne toujours l'allocation stable optimale pour les employés est caractérisé comme étant l ‘unique mécanisme " efficace " ou " monotone " ou " strategy-proof.

Stable Allocation Mechanism

Le problème d'allocations stables généralise les problèmes d'affectations stables (" one-to-one ", " one-to-many " ou " many-to-many ") à l'attribution de quantités réelles ou d'heures. Il existe deux ensembles d'agents distincts, un ensemble I " employés " et un ensemble J " employeurs " où chaque agent a un ordre de préférences sur les agents de l'ensemble opposé et chacun a un certain nombre d'heures. Comme dans les cas spécifiques, le problème d'allocations stables peut contenir un nombre exponentiel de stables (quoique dans le cas " générique " il admet exactement une allocation stable). Un mécanisme est une fonction qui sélectionne exactement une allocation stable pour n'importe quel problème. Le mécanisme " optimal-employés " qui sélectionne toujours l'allocation stable optimale pour les employés est caractérisé comme étant l ‘unique mécanisme " efficace " ou " monotone " ou " strategy-proof. "Affectation stable;Mariage stable;Couplage stable;Transport ordinal;Problème d'admission;Many-to-many matching;Two sided market

Dynamics of the Amplitude-to-Phase Coupling of 1.5µm High Bandwidth Commercial Photodiodes

National audienceWe investigate the power-to-phase coupling in two commercial high bandwidth P-i-N near-IR photodetectors. We observe that a sudden change of the optical power induces a transient of the phase of the 20 GHz signal, at different time scales. The temperature rise of the photodetector junction is likely to be involved in this dynamical behaviour. The value of the bias voltage applied to the photodetector appears to control the size of the phase transients, as well as the optical power for which the slope of the amplitude-to-phase coupling cancels. These results are important in optimising RF optical links

Phase measurement of a microwave optical modulation: characterisation and reduction of amplitude-to-phase conversion in 1.5 µm high bandwidth photodiodes

En attente de publication papier; Lien vers l'éditeur: http://ieeexplore.ieee.org/xpl/articleDetails.jsp? arnumber=6775285&sortType%3Dasc_p_Sequence% 26filter%3DAND%28p_IS_Number%3A4357488%29International audienceHigh accuracy and low noise measurement of the phase of a microwave signal requires that spurious contributions are adequately dealt with. In this paper we investigate the power-to-phase coupling in two commercial high bandwidth P-I-N, near-IR photodetectors. We observe that a sudden change of the optical power induces a transient of the phase of the 20 GHz signal, at different time scales. The temperature rise of the photodetector junction is likely to be involved in this dynamical behaviour. The value of the bias voltage applied to the photodetector appears to control the size of the phase transients, as well as the optical power for which the slope of the amplitude-to-phase coupling cancels. The most efficient way to reduce amplitude to phase couplings consists in implementing optical demodulation, instead of electrical demodulation, of the microwave signal

Robust bounded-error tracking in wireless sensor networks

International audienceA wireless sensor network (WSN) consists of spatially distributed sensors connected via a wireless link. Sensors may be designed for pressure, temperature, sound, vibration, motion... This paper considers the problem of target tracking in a WSN. This problem is especially challenging in presence of measurements which are outliers. Two algorithms for target tracking robust to outliers are proposed. They only assume that the maximum number of outliers is known. Based on interval analysis, these algorithms perform a set-membership estimation using either SIVIA or a combinatorial technique. In both cases, sets of boxes guaranteed to contain the actual target location are provided

Robust Interval-Based Localization Algorithms for Mobile Sensor Networks

International audienceThis paper considers the localization problem in mobile sensor networks. Such a problem is a challenging task, especially when measurements exchanged between sensors may contain outliers, \textit{i.e.}, data not matching the observation model. This paper proposes two algorithms robust to outliers. These algorithms perform a set-membership estimation, where only the maximal number of outliers is required to be known. Using these algorithms, estimates consist of sets of boxes whose union surely contains the correct location of the sensor, provided that the considered hypotheses are satisfied. This paper proposes as well a technique for evaluating the number of outliers to be robust to. In order to corroborate the efficiency of both algorithms, a comparison of their performances is performed in simulations using Matlab