5 research outputs found
On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples
We show a concise extension of the monotone stability approach to backward
stochastic differential equations (BSDEs) that are jointly driven by a Brownian
motion and a random measure for jumps, which could be of infinite activity with
a non-deterministic and time inhomogeneous compensator. The BSDE generator
function can be non convex and needs not to satisfy global Lipschitz conditions
in the jump integrand. We contribute concrete criteria, that are easy to
verify, for results on existence and uniqueness of bounded solutions to BSDEs
with jumps, and on comparison and a-priori -bounds. Several
examples and counter examples are discussed to shed light on the scope and
applicability of different assumptions, and we provide an overview of major
applications in finance and optimal control.Comment: 28 pages. Added DOI
https://link.springer.com/chapter/10.1007%2F978-3-030-22285-7_1 for final
publication, corrected typo (missing gamma) in example 4.1
Entropy coherent and entropy convex measures of risk
We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized version, respectively, of) the popular maxmin expected utility theory of Gilboa and Schmeidler [12] whenever the negative certainty equivalents are translation invariant. In addition, we derive the dual conjugate function for entropy coherent and entropy convex measures of risk, and prove their distribution invariant representation.
Keywords: Robust preferences; Convex risk measures; Exponential utility; Relative entropy; Translation invariance; Convexity