4,305 research outputs found
A Benchmark Approach to Risk-Minimization under Partial Information
In this paper we study a risk-minimizing hedging problem for a semimartingale
incomplete financial market where d+1 assets are traded continuously and whose
price is expressed in units of the num\'{e}raire portfolio. According to the
so-called benchmark approach, we investigate the (benchmarked) risk-minimizing
strategy in the case where there are restrictions on the available information.
More precisely, we characterize the optimal strategy as the integrand appearing
in the Galtchouk-Kunita-Watanabe decomposition of the benchmarked claim under
partial information and provide its description in terms of the integrands in
the classical Galtchouk-Kunita-Watanabe decomposition under full information
via dual predictable projections. Finally, we apply the results in the case of
a Markovian jump-diffusion driven market model where the assets prices dynamics
depend on a stochastic factor which is not observable by investors.Comment: 31 page
Bartering integer commodities with exogenous prices
The analysis of markets with indivisible goods and fixed exogenous prices has
played an important role in economic models, especially in relation to wage
rigidity and unemployment. This research report provides a mathematical and
computational details associated to the mathematical programming based
approaches proposed by Nasini et al. (accepted 2014) to study pure exchange
economies where discrete amounts of commodities are exchanged at fixed prices.
Barter processes, consisting in sequences of elementary reallocations of couple
of commodities among couples of agents, are formalized as local searches
converging to equilibrium allocations. A direct application of the analyzed
processes in the context of computational economics is provided, along with a
Java implementation of the approaches described in this research report.Comment: 30 pages, 5 sections, 10 figures, 3 table
A Fourier analytic approach to the problem of mutually unbiased bases
We give an entirely new approach to the problem of mutually unbiased bases
(MUBs), based on a Fourier analytic technique in additive combinatorics. The
method provides a short and elegant generalization of the fact that there are
at most MUBs in \Co^d. It may also yield a proof that no complete
system of MUBs exists in some composite dimensions -- a long standing open
problem.Comment: 11 page
Primitive Zonotopes
We introduce and study a family of polytopes which can be seen as a
generalization of the permutahedron of type . We highlight connections
with the largest possible diameter of the convex hull of a set of points in
dimension whose coordinates are integers between and , and with the
computational complexity of multicriteria matroid optimization.Comment: The title was slightly modified, and the determination of the
computational complexity of multicriteria matroid optimization was adde
Three-point bounds for energy minimization
Three-point semidefinite programming bounds are one of the most powerful
known tools for bounding the size of spherical codes. In this paper, we use
them to prove lower bounds for the potential energy of particles interacting
via a pair potential function. We show that our bounds are sharp for seven
points in RP^2. Specifically, we prove that the seven lines connecting opposite
vertices of a cube and of its dual octahedron are universally optimal. (In
other words, among all configurations of seven lines through the origin, this
one minimizes energy for all potential functions that are completely monotonic
functions of squared chordal distance.) This configuration is the only known
universal optimum that is not distance regular, and the last remaining
universal optimum in RP^2. We also give a new derivation of semidefinite
programming bounds and present several surprising conjectures about them.Comment: 30 page
Detector-Agnostic Phase-Space Distributions
The representation of quantum states via phase-space functions constitutes an
intuitive technique to characterize light. However, the reconstruction of such
distributions is challenging as it demands specific types of detectors and
detailed models thereof to account for their particular properties and
imperfections. To overcome these obstacles, we derive and implement a
measurement scheme that enables a reconstruction of phase-space distributions
for arbitrary states whose functionality does not depend on the knowledge of
the detectors, thus defining the notion of detector-agnostic phase-space
distributions. Our theory presents a generalization of well-known phase-space
quasiprobability distributions, such as the Wigner function. We implement our
measurement protocol, using state-of-the-art transition-edge sensors without
performing a detector characterization. Based on our approach, we reveal the
characteristic features of heralded single- and two-photon states in phase
space and certify their nonclassicality with high statistical significance
Lecture notes: Semidefinite programs and harmonic analysis
Lecture notes for the tutorial at the workshop HPOPT 2008 - 10th
International Workshop on High Performance Optimization Techniques (Algebraic
Structure in Semidefinite Programming), June 11th to 13th, 2008, Tilburg
University, The Netherlands.Comment: 31 page
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