Samuel Drapeau

Risk Preferences and Their Robust Representation

To address the plurality of interpretations of the subjective notion of risk, we describe it by means of a risk order and concentrate on the context invariant features of diversification and monotonicity. Our main results are uniquely characterized robust representations of lower semicontinuous risk orders on vector spaces and convex sets. This representation covers most instruments related to risk and allows for a differentiated interpretation depending on the underlying context that is illustrated in different settings: for random variables, risk perception can be interpreted as model risk, and we compute among others the robust representation of the economic index of riskiness. For lotteries, risk perception can be viewed as distributional risk and we study the “value at risk.” For consumption patterns, which excerpt an intertemporality dimension in risk perception, we provide an interpretation in terms of discounting risk and discuss some examples.

The Algebra of Conditional Sets and the Concepts of Conditional Topology and Compactness

Abstract The concepts of a conditional set, a conditional inclusion relation and a conditional Cartesian product are introduced. The resulting conditional set theory is sufficiently rich in order to construct a conditional topology, a conditional real and functional analysis indicating the possibility of a mathematical discourse based on conditional sets. It is proved that the conditional power set is a complete Boolean algebra, and a conditional version of the axiom of choice, the ultrafilter lemma, Tychonoffs theorem, the Borel–Lebesgue theorem, the Hahn–Banach theorem, the Banach–Alaoglu theorem and the Krein–Smulian theorem are shown.

Minimal supersolutions of convex BSDEs

We study the nonlinear operator of mapping the terminal value

Dynamic Assessment Indices

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Dual Representation of Minimal Supersolutions of Convex BSDEs

to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in

Multivariate Shortfall Risk Allocation and Systemic Risk

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A Fourier Approach to the Computation of Conditional Value-at-Risk and Optimized Certainty Equivalents

, convex in

Brouwer fixed point theorem in (L0)d

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Weak Closedness of Monotone Sets of Lotteries and Robust Representation of Risk Preferences

, jointly lower semicontinuous and bounded below by an affine function of the control variable

A note on robust representations of law-invariant quasiconvex functions

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