186 research outputs found

    Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

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    To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consum- ing method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computa- tional effort in the approximation while, at the same time, the accuracy increasesPeer ReviewedPreprin

    Notes paleozoiques del Pirineu Axial

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    Confinement of spacecraft swarms in J2-perturbed orbits about the earth

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    There have been studies of the reliability of a swarm [3], based on nano-satellites, that give a study for the num- ber of satellites that can be working as a period of time, with good results for a 5-10 anys time step. The strategies to control the swarm are based in three main concepts. The first one studies the global movement of the swarm as the ones that we can find in nature [5], where each of the spacecraft has behavior depending on the position and velocity of closest neighbors. The sec- ond one are the strategies that include the provision of collision-free orbits for long periods of time[1]. Finally , there is the strategy to keep the relative distance between spacecraft [2]. The main contribution of this paper is the adapta- tion of a methodology proposed for reconfigurations of spacecraft [6] to swarms, taking into account that the higher complexity of the problem needs some adjuste- ments. These adjustements are based on the strategies of swarms in nature (there are only reconfigurations based on the neighbour states). The statement of the problem is to calculate the cost to maintain the spacecraft of the swarm for a year in a sphere of radius R for a year, avoid- ing collisions and minimizing the fuel usagePeer ReviewedPostprint (published version

    Reconfiguration of spacecraft formations in the vicinity of libration points

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    Formation °ying is an important concept demanding reliable and accurate techniques for the recon¯gura- tion or the deployment of the spacecraft. This paper is a contribution to these set of techniques considering a ¯nite element approach. The formulation allows to compute proximity maneuvers for the spacecraft and, at the same time, to incorporate optimal control techniques which include collision avoidance or many other types of constraints. The computations have been carried out about libration point orbits of the Sun-Earth system and using linearized equations about a nonlinear nominal base orbit. The trajectories obtained for this model have been corrected considering a full nonlinear model (JPL-ephemeris). Also random errors have been added to the nominal recon¯guration maneuvers to simulate small thrust errors. The presented methodology proves to be robust in both the computation of the nominal recon¯guration maneuvers and in the correction of the perturbations.Postprint (published version

    Homoclinic and heteroclinic transfer trajectories between Lyapunov orbits in the Sun-Earth and Earth-Moon systems

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    In this paper a method for finding homoclinic and heteroclinic connections between Lyapunov orbits using invariant manifolds in a given energy surface of the planar restricted circular three body problem is developed. Moreover, the systematic application of this method to a range of Jacobi constants provides a classification of the connections in bifurcation families. The models used correspond to the Sun-Earth+Moon and the Earth-Moon cases

    Methodology and estimation costs for proximity maneuvering spacecraft formations in the vicinity of libration points

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    The aim of this paper is to study and provide estimations of the cost of reconfiguration maneuvers in the neighbor- hood of L1 and L2 libration points of the Sun-Earth system. The problem is considered as a function of the parameters of the formation (baseline length, security distances, orientation, reconfiguration time) and simple formulae to evaluate the costs are given.Postprint (published version

    Spacecraft formations reconfiguration using finite element methodology with adaptive remeshing

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    We present a methodology to compute trajectories for formation °ying recon¯g- uration problems using a methodology based on ¯nite elements: FEFF (Finite Elements for Formation Flying). In this paper we center ourselves on the obtention of optimal meshes using adaptive remeshing. As an application we show how adaptive remeshing is applied to two kinds of recon¯gurations: a class where is known that a bang-bang control is the optimal solution and another class where bang-bang would end up in collision. In the ¯rst case the methodology tends to the optimal bang-bang, while in the second one, tends to a low thrust control. Finally, we update the trajectories obtained with FEFF and adaptive remeshing to the JPL-ephemeris model to test the reliability of the methodology.Postprint (published version

    Dynamics in the centre manifold around equilibrium points in periodically perturbed three-body problems

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    A new application of the parameterization method is pre- sented to compute invariant manifolds about the equilib- rium points of Periodically Perturbed Three-Body Problems ( PPTBP ). These techniques are applied to obtain high-order semi-numerical approximations of the center manifolds abo ut the points L 1 , 2 of the Sun-perturbed Earth-Moon Quasi- Bicicular Problem ( QBCP ), which is a particular case of PPTBP . The quality of these approximations is compared with results obtained using equivalents of previous normal form procedures. Then, the parameterization is used to ini- tialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturb ed dynamics near the equilibrium pointsPostprint (published version

    Global analysis of direct transfers from lunar orbits to sun-earth libration point regimes

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    In this paper we look forward to obtain a global picture of simple transfer opportunities from Lunar to Sun-Earth libration orbits, useful for a preliminary design of these mission scenarios. Considering the trajectory of the Chinese Change’2 spacecraft as a reference case, the main transfer families are characterized and classified. In a second step, the results are analyzed and extended to departures from more general families of orbits about the Moon. Finally, we also include a preliminary sensitivity analysis of the first transfer correction maneuver (TCM1) to cancel injection errors. The methodology is of general applicability to the transfer analysis involving libration point final orbits in other general multi-body restricted systems.Peer ReviewedPostprint (author's final draft
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