186 research outputs found
Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation
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
Confinement of spacecraft swarms in J2-perturbed orbits about the earth
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
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 ÂŻnite 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 reconÂŻguration maneuvers to simulate small thrust errors. The presented
methodology proves to be robust in both the computation of the nominal reconÂŻguration 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
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
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
We present a methodology to compute trajectories for formation °ying recon¯g-
uration problems using a methodology based on ÂŻnite 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 reconÂŻgurations: 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 ÂŻrst 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
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
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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