32,437 research outputs found
Sensitivity analysis in calculus of variations. Some applications
This paper deals with the problem of sensitivity analysis in calculus of variations. A perturbation technique is applied to derive the boundary value problem and the system of equations that allow us to obtain the partial derivatives (sensitivities) of the objective function value and the primal and dual optimal solutions with respect to all parameters. Two examples of applications, a simple mathematical problem and a slope stability analysis problem, are used to illustrate the proposed method
Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus
This study introduces computation of option sensitivities (Greeks) using the
Malliavin calculus under the assumption that the underlying asset and interest
rate both evolve from a stochastic volatility model and a stochastic interest
rate model, respectively. Therefore, it integrates the recent developments in
the Malliavin calculus for the computation of Greeks: Delta, Vega, and Rho and
it extends the method slightly. The main results show that Malliavin calculus
allows a running Monte Carlo (MC) algorithm to present numerical
implementations and to illustrate its effectiveness. The main advantage of this
method is that once the algorithms are constructed, they can be used for
numerous types of option, even if their payoff functions are not
differentiable.Comment: Published at https://doi.org/10.15559/18-VMSTA100 in the Modern
Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA)
by VTeX (http://www.vtex.lt/
Dirichlet forms methods, an application to the propagation of the error due to the Euler scheme
We present recent advances on Dirichlet forms methods either to extend
financial models beyond the usual stochastic calculus or to study stochastic
models with less classical tools. In this spirit, we interpret the asymptotic
error on the solution of an sde due to the Euler scheme in terms of a Dirichlet
form on the Wiener space, what allows to propagate this error thanks to
functional calculus.Comment: 15
A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution
To overcome the weakness of a total variation based model for image
restoration, various high order (typically second order) regularization models
have been proposed and studied recently. In this paper we analyze and test a
fractional-order derivative based total -order variation model, which
can outperform the currently popular high order regularization models. There
exist several previous works using total -order variations for image
restoration; however first no analysis is done yet and second all tested
formulations, differing from each other, utilize the zero Dirichlet boundary
conditions which are not realistic (while non-zero boundary conditions violate
definitions of fractional-order derivatives). This paper first reviews some
results of fractional-order derivatives and then analyzes the theoretical
properties of the proposed total -order variational model rigorously.
It then develops four algorithms for solving the variational problem, one based
on the variational Split-Bregman idea and three based on direct solution of the
discretise-optimization problem. Numerical experiments show that, in terms of
restoration quality and solution efficiency, the proposed model can produce
highly competitive results, for smooth images, to two established high order
models: the mean curvature and the total generalized variation.Comment: 26 page
Sharp interface limit for a phase field model in structural optimization
We formulate a general shape and topology optimization problem in structural
optimization by using a phase field approach. This problem is considered in
view of well-posedness and we derive optimality conditions. We relate the
diffuse interface problem to a perimeter penalized sharp interface shape
optimization problem in the sense of -convergence of the reduced
objective functional. Additionally, convergence of the equations of the first
variation can be shown. The limit equations can also be derived directly from
the problem in the sharp interface setting. Numerical computations demonstrate
that the approach can be applied for complex structural optimization problems
Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
A human respiratory syncytial virus surveillance system was implemented in
Florida in 1999, to support clinical decision-making for prophylaxis of
premature newborns. Recently, a local periodic SEIRS mathematical model was
proposed in [Stat. Optim. Inf. Comput. 6 (2018), no.1, 139--149] to describe
real data collected by Florida's system. In contrast, here we propose a
non-local fractional (non-integer) order model. A fractional optimal control
problem is then formulated and solved, having treatment as the control.
Finally, a cost-effectiveness analysis is carried out to evaluate the cost and
the effectiveness of proposed control measures during the intervention period,
showing the superiority of obtained results with respect to previous ones.Comment: This is a preprint of a paper whose final and definite form is with
'Chaos, Solitons & Fractals', available from
[http://www.elsevier.com/locate/issn/09600779]. Submitted 23-July-2018;
Revised 14-Oct-2018; Accepted 15-Oct-2018. arXiv admin note: substantial text
overlap with arXiv:1801.0963
A survey on fractional order control techniques for unmanned aerial and ground vehicles
In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade
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