1,704 research outputs found
Measuring risk with multiple eligible assets
The risk of financial positions is measured by the minimum amount of capital
to raise and invest in eligible portfolios of traded assets in order to meet a
prescribed acceptability constraint. We investigate nondegeneracy, finiteness
and continuity properties of these risk measures with respect to multiple
eligible assets. Our finiteness and continuity results highlight the interplay
between the acceptance set and the class of eligible portfolios. We present a
simple, alternative approach to the dual representation of convex risk measures
by directly applying to the acceptance set the external characterization of
closed, convex sets. We prove that risk measures are nondegenerate if and only
if the pricing functional admits a positive extension which is a supporting
functional for the underlying acceptance set, and provide a characterization of
when such extensions exist. Finally, we discuss applications to set-valued risk
measures, superhedging with shortfall risk, and optimal risk sharing
Beyond cash-additive risk measures: when changing the num\'{e}raire fails
We discuss risk measures representing the minimum amount of capital a
financial institution needs to raise and invest in a pre-specified eligible
asset to ensure it is adequately capitalized. Most of the literature has
focused on cash-additive risk measures, for which the eligible asset is a
risk-free bond, on the grounds that the general case can be reduced to the
cash-additive case by a change of numeraire. However, discounting does not work
in all financially relevant situations, typically when the eligible asset is a
defaultable bond. In this paper we fill this gap allowing for general eligible
assets. We provide a variety of finiteness and continuity results for the
corresponding risk measures and apply them to risk measures based on
Value-at-Risk and Tail Value-at-Risk on spaces, as well as to shortfall
risk measures on Orlicz spaces. We pay special attention to the property of
cash subadditivity, which has been recently proposed as an alternative to cash
additivity to deal with defaultable bonds. For important examples, we provide
characterizations of cash subadditivity and show that, when the eligible asset
is a defaultable bond, cash subadditivity is the exception rather than the
rule. Finally, we consider the situation where the eligible asset is not
liquidly traded and the pricing rule is no longer linear. We establish when the
resulting risk measures are quasiconvex and show that cash subadditivity is
only compatible with continuous pricing rules
Feller semigroups, Lp-sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols
The question of extending L-p-sub-Markovian semigroups to the spaces L-q, q > P, and the interpolation of LP-sub-Markovian semigroups with Feller semigroups is investigated. The structure of generators of L-p-sub-Markovian semigroups is studied. Subordination in the sense of Bochner is used to discuss the construction of refinements of L-p-sub-Markovian semigroups. The role played by some function spaces which are domains of definition for L-p-generators is pointed out. The problem of regularising powers of generators as well as some perturbation results are discussed
The Emma Family Backyard Deck – Thousand Oaks, CA
This paper outlines the planning, design, and construction of an 80 square foot deck/outdoor patio. The main purpose of this project was to assist an elder couple fund and construct a new deck in their backyard. Due to the current world pandemic, COVID-19 the Emma Family was practicing social distancing and adhering to the State and County wide stay at home order. The project plan was to design a deck for Emma family in the design, construction it and receive funding. The deck was a rectangular 8’ x 10’ and raised 6” off the ground. In addition to the deck the project also consisted of a removable housing unit for the main sprinkler and water line. This paper will focus on the preconstruction phase, construction phase, lessons learned, and how this knowledge will be applied to the construction industry
Sobolev Spaces on Non Smooth Domains and Dirichlet Forms Related to Subordinate Reflecting Diffusions
Characterisations of function spaces of generalised smoothness
We investigate function spaces of generalised smoothness of Besov and Triebel-Lizorkin type. Equivalent quasi-norms in terms of maximal functions and local means are given. An atomic decomposition theorem for this type of spaces is prove
Anlegen mit KI - Herausforderung und Chance
Künstliche Intelligenz hat die Effizienz der Datenanalyse revolutioniert und bietet die Möglichkeit, das Investment Research und Portfoliomanagement zu automatisieren. Ihr Einsatz ist aber kein uneingeschränkter Erfolgsgarant
Anisotropic function spaces, fractals, and spectra of some elliptic and semi-elliptic operators
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