56 research outputs found
Minimal supersolutions of convex BSDEs
We study the nonlinear operator of mapping the terminal value to the
corresponding minimal supersolution of a backward stochastic differential
equation with the generator being monotone in , convex in , jointly lower
semicontinuous and bounded below by an affine function of the control variable
. We show existence, uniqueness, monotone convergence, Fatou's lemma and
lower semicontinuity of this operator. We provide a comparison principle for
minimal supersolutions of BSDEs.Comment: Published in at http://dx.doi.org/10.1214/13-AOP834 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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
Dynamic Assessment Indices
This paper provides a unified framework, which allows, in particular, to
study the structure of dynamic monetary risk measures and dynamic acceptability
indices. The main mathematical tool, which we use here, and which allows us to
significantly generalize existing results is the theory of -modules. In
the first part of the paper we develop the general theory and provide a robust
representation of conditional assessment indices, and in the second part we
apply this theory to dynamic acceptability indices acting on stochastic
processes.Comment: 39 page
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