578 research outputs found
On Monotonicity and Propagation of Order Properties
In this paper, a link between monotonicity of deterministic dynamical systems
and propagation of order by Markov processes is established. The order
propagation has received considerable attention in the literature, however,
this notion is still not fully understood. The main contribution of this paper
is a study of the order propagation in the deterministic setting, which
potentially can provide new techniques for analysis in the stochastic one. We
take a close look at the propagation of the so-called increasing and increasing
convex orders. Infinitesimal characterisations of these orders are derived,
which resemble the well-known Kamke conditions for monotonicity. It is shown
that increasing order is equivalent to the standard monotonicity, while the
class of systems propagating the increasing convex order is equivalent to the
class of monotone systems with convex vector fields. The paper is concluded by
deriving a novel result on order propagating diffusion processes and an
application of this result to biological processes.Comment: Part of the paper is to appear in American Control Conference 201
Proof mining in metric fixed point theory and ergodic theory
In this survey we present some recent applications of proof mining to the
fixed point theory of (asymptotically) nonexpansive mappings and to the
metastability (in the sense of Terence Tao) of ergodic averages in uniformly
convex Banach spaces.Comment: appeared as OWP 2009-05, Oberwolfach Preprints; 71 page
Directed Subdifferentiable Functions and the Directed Subdifferential without Delta-Convex Structure
We show that the directed subdifferential introduced for differences of
convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from
the directional derivative without using any information on the DC structure of
the function. The new definition extends to a more general class of functions,
which includes Lipschitz functions definable on o-minimal structure and
quasidifferentiable functions.Comment: 30 pages, 3 figure
Multivariate Shortfall Risk Allocation and Systemic Risk
The ongoing concern about systemic risk since the outburst of the global
financial crisis has highlighted the need for risk measures at the level of
sets of interconnected financial components, such as portfolios, institutions
or members of clearing houses. The two main issues in systemic risk measurement
are the computation of an overall reserve level and its allocation to the
different components according to their systemic relevance. We develop here a
pragmatic approach to systemic risk measurement and allocation based on
multivariate shortfall risk measures, where acceptable allocations are first
computed and then aggregated so as to minimize costs. We analyze the
sensitivity of the risk allocations to various factors and highlight its
relevance as an indicator of systemic risk. In particular, we study the
interplay between the loss function and the dependence structure of the
components. Moreover, we address the computational aspects of risk allocation.
Finally, we apply this methodology to the allocation of the default fund of a
CCP on real data.Comment: Code, results and figures can also be consulted at
https://github.com/yarmenti/MSR
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