10,607 research outputs found
Set-valued shortfall and divergence risk measures
Risk measures for multivariate financial positions are studied in a
utility-based framework. Under a certain incomplete preference relation,
shortfall and divergence risk measures are defined as the optimal values of
specific set minimization problems. The dual relationship between these two
classes of multivariate risk measures is constructed via a recent Lagrange
duality for set optimization. In particular, it is shown that a shortfall risk
measure can be written as an intersection over a family of divergence risk
measures indexed by a scalarization parameter. Examples include set-valued
versions of the entropic risk measure and the average value at risk. As a
second step, the minimization of these risk measures subject to trading
opportunities is studied in a general convex market in discrete time. The
optimal value of the minimization problem, called the market risk measure, is
also a set-valued risk measure. A dual representation for the market risk
measure that decomposes the effects of the original risk measure and the
frictions of the market is proved
A Minty variational principle for set optimization
Extremal problems are studied involving an objective function with values in
(order) complete lattices of sets generated by so called set relations.
Contrary to the popular paradigm in vector optimization, the solution concept
for such problems, introduced by F. Heyde and A. L\"ohne, comprises the
attainment of the infimum as well as a minimality property. The main result is
a Minty type variational inequality for set optimization problems which
provides a sufficient optimality condition under lower semicontinuity
assumptions and a necessary condition under appropriate generalized convexity
assumptions. The variational inequality is based on a new Dini directional
derivative for set-valued functions which is defined in terms of a "lattice
difference quotient": A residual operation in a lattice of sets replaces the
inverse addition in linear spaces. Relationships to families of scalar problems
are pointed out and used for proofs: The appearance of improper scalarizations
poses a major difficulty which is dealt with by extending known scalar results
such as Diewert's theorem to improper functions
Panel Discussion - Management of Eurasian watermilfoil in the United States using native insects: State regulatory and management issues
While researchers have evaluated the potential of native
insect herbivores to manage nonindigenous aquatic plant
species such as Eurasian watermilfoil (
Myriophyllum spicatum
L.), the practical matters of regulatory compliance and implementation
have been neglected. A panel of aquatic nuisance
species program managers from three state natural
resource management agencies (Minnesota, Vermont and
Washington) discussed their regulatory and policy concerns.
In addition, one ecological consultant attempting to market
one of the native insects to manage Eurasian watermilfoil
added his perspective on the special challenges of distributing
a native biological control agent for management of Eurasian
watermilfoil
Localized and Expanding Entire Solutions of Reaction-Diffusion Equations
This paper is concerned with the spatio-temporal dynamics of nonnegative
bounded entire solutions of some reaction-diffusion equations in R N in any
space dimension N. The solutions are assumed to be localized in the past. Under
certain conditions on the reaction term, the solutions are then proved to be
time-independent or heteroclinic connections between different steady states.
Furthermore, either they are localized uniformly in time, or they converge to a
constant steady state and spread at large time. This result is then applied to
some specific bistable-type reactions
Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in \Er^2
In this paper, we prove even symmetry of monotone traveling wave solutions to
the balanced Allen-Cahn equation in the entire plane. Related results for the
unbalanced Allen-Cahn equation are also discussed
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