8,230 research outputs found
Linear vector optimization and European option pricing under proportional transaction costs
A method for pricing and superhedging European options under proportional
transaction costs based on linear vector optimisation and geometric duality
developed by Lohne & Rudloff (2014) is compared to a special case of the
algorithms for American type derivatives due to Roux & Zastawniak (2014). An
equivalence between these two approaches is established by means of a general
result linking the support function of the upper image of a linear vector
optimisation problem with the lower image of the dual linear optimisation
problem
A Parametric Simplex Algorithm for Linear Vector Optimization Problems
In this paper, a parametric simplex algorithm for solving linear vector
optimization problems (LVOPs) is presented. This algorithm can be seen as a
variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different
from it, the proposed algorithm works in the parameter space and does not aim
to find the set of all efficient solutions. Instead, it finds a solution in the
sense of Loehne [16], that is, it finds a subset of efficient solutions that
allows to generate the whole frontier. In that sense, it can also be seen as a
generalization of the parametric self-dual simplex algorithm, which originally
is designed for solving single objective linear optimization problems, and is
modified to solve two objective bounded LVOPs with the positive orthant as the
ordering cone in Ruszczynski and Vanderbei [21]. The algorithm proposed here
works for any dimension, any solid pointed polyhedral ordering cone C and for
bounded as well as unbounded problems. Numerical results are provided to
compare the proposed algorithm with an objective space based LVOP algorithm
(Benson algorithm in [13]), that also provides a solution in the sense of [16],
and with Evans-Steuer algorithm [12]. The results show that for non-degenerate
problems the proposed algorithm outperforms Benson algorithm and is on par with
Evan-Steuer algorithm. For highly degenerate problems Benson's algorithm [13]
excels the simplex-type algorithms; however, the parametric simplex algorithm
is for these problems computationally much more efficient than Evans-Steuer
algorithm.Comment: 27 pages, 4 figures, 5 table
Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems
Two approximation algorithms for solving convex vector optimization problems
(CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual
problem simultaneously. The first algorithm is an extension of Benson's outer
approximation algorithm, and the second one is a dual variant of it. Both
algorithms provide an inner as well as an outer approximation of the (upper and
lower) images. Only one scalar convex program has to be solved in each
iteration. We allow objective and constraint functions that are not necessarily
differentiable, allow solid pointed polyhedral ordering cones, and relate the
approximations to an appropriate \epsilon-solution concept. Numerical examples
are provided
Particle Density Estimation with Grid-Projected Adaptive Kernels
The reconstruction of smooth density fields from scattered data points is a
procedure that has multiple applications in a variety of disciplines, including
Lagrangian (particle-based) models of solute transport in fluids. In random
walk particle tracking (RWPT) simulations, particle density is directly linked
to solute concentrations, which is normally the main variable of interest, not
just for visualization and post-processing of the results, but also for the
computation of non-linear processes, such as chemical reactions. Previous works
have shown the superiority of kernel density estimation (KDE) over other
methods such as binning, in terms of its ability to accurately estimate the
"true" particle density relying on a limited amount of information. Here, we
develop a grid-projected KDE methodology to determine particle densities by
applying kernel smoothing on a pilot binning; this may be seen as a "hybrid"
approach between binning and KDE. The kernel bandwidth is optimized locally.
Through simple implementation examples, we elucidate several appealing aspects
of the proposed approach, including its computational efficiency and the
possibility to account for typical boundary conditions, which would otherwise
be cumbersome in conventional KDE
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