224 research outputs found
Law-Invariant Return and Star-Shaped Risk Measures
This paper presents novel characterization results for classes of
law-invariant star-shaped functionals. We begin by establishing
characterizations for positively homogeneous and star-shaped functionals that
exhibit second- or convex-order stochastic dominance consistency. Building on
these characterizations, we proceed to derive Kusuoka-type representations for
these functionals, shedding light on their mathematical structure and intimate
connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer
representations of general law-invariant star-shaped functionals as
robustifications of Value-at-Risk. Notably, our results are versatile,
accommodating settings that may, or may not, involve monotonicity and/or
cash-additivity. All of these characterizations are developed within a general
locally convex topological space of random variables, ensuring the broad
applicability of our results in various financial, insurance and probabilistic
contexts
Dynamic Return and Star-Shaped Risk Measures via BSDEs
This paper establishes characterization results for dynamic return and
star-shaped risk measures induced via backward stochastic differential
equations (BSDEs). We first characterize a general family of static star-shaped
functionals in a locally convex Fr\'echet lattice. Next, employing the
Pasch-Hausdorff envelope, we build a suitable family of convex drivers of BSDEs
inducing a corresponding family of dynamic convex risk measures of which the
dynamic return and star-shaped risk measures emerge as the essential minimum.
Furthermore, we prove that if the set of star-shaped supersolutions of a BSDE
is not empty, then there exists, for each terminal condition, at least one
convex BSDE with a non-empty set of supersolutions, yielding the minimal
star-shaped supersolution. We illustrate our theoretical results in a few
examples and demonstrate their usefulness in two applications, to capital
allocation and portfolio choice
Inf-convolution of G-expectations
In this paper we will discuss the optimal risk transfer problems when risk
measures are generated by G-expectations, and we present the relationship
between inf-convolution of G-expectations and the inf-convolution of drivers G.Comment: 23 page
A general theory of Finite State Backward Stochastic Difference Equations
By analogy with the theory of Backward Stochastic Differential Equations, we
define Backward Stochastic Difference Equations on spaces related to discrete
time, finite state processes. This paper considers these processes as
constructions in their own right, not as approximations to the continuous case.
We establish the existence and uniqueness of solutions under weaker assumptions
than are needed in the continuous time setting, and also establish a comparison
theorem for these solutions. The conditions of this theorem are shown to
approximate those required in the continuous time setting. We also explore the
relationship between the driver and the set of solutions; in particular, we
determine under what conditions the driver is uniquely determined by the
solution. Applications to the theory of nonlinear expectations are explored,
including a representation result.Comment: 25 pages, final preprint prior to refereein
Clinical practice of language fMRI in epilepsy centers: a European survey and conclusions by the ESNR Epilepsy Working Group
Purpose: To assess current clinical practices throughout Europe with respect to acquisition, implementation, evaluation, and interpretation of language functional MRI (fMRI) in epilepsy patients. Methods: An online survey was emailed to all European Society of Neuroradiology members (n = 1662), known associates (n = 6400), and 64 members of European Epilepsy network. The questionnaire featured 40 individual items on demographic data, clinical practice and indications, fMRI paradigms, radiological workflow, data post-processing protocol, and reporting. Results: A total of 49 non-duplicate entries from European centers were received from 20 countries. Of these, 73.5% were board-certified neuroradiologists and 69.4% had an in-house epilepsy surgery program. Seventy-one percent of centers performed fewer than five scans per month for epilepsy. The most frequently used paradigms were phonemic verbal fluency (47.7%) and audi
Representation of the penalty term of dynamic concave utilities
In this paper we will provide a representation of the penalty term of general
dynamic concave utilities (hence of dynamic convex risk measures) by applying
the theory of g-expectations.Comment: An updated version is published in Finance & Stochastics. The final
publication is available at http://www.springerlink.co
A study of patent thickets
Report analysing whether entry of UK enterprises into patenting in a technology area is affected by patent thickets in the technology area
Recent progress in random metric theory and its applications to conditional risk measures
The purpose of this paper is to give a selective survey on recent progress in
random metric theory and its applications to conditional risk measures. This
paper includes eight sections. Section 1 is a longer introduction, which gives
a brief introduction to random metric theory, risk measures and conditional
risk measures. Section 2 gives the central framework in random metric theory,
topological structures, important examples, the notions of a random conjugate
space and the Hahn-Banach theorems for random linear functionals. Section 3
gives several important representation theorems for random conjugate spaces.
Section 4 gives characterizations for a complete random normed module to be
random reflexive. Section 5 gives hyperplane separation theorems currently
available in random locally convex modules. Section 6 gives the theory of
random duality with respect to the locally convex topology and in
particular a characterization for a locally convex module to be
prebarreled. Section 7 gives some basic results on convex
analysis together with some applications to conditional risk measures. Finally,
Section 8 is devoted to extensions of conditional convex risk measures, which
shows that every representable type of conditional convex risk
measure and every continuous type of convex conditional risk measure
() can be extended to an type
of lower semicontinuous conditional convex risk measure and an
type of continuous
conditional convex risk measure (), respectively.Comment: 37 page
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