Convex measures of risk and trading constraints

Lp solutions of backward stochastic differential equations with jumps

“…In [74], we first derive a strict comparison theorem for L p −solutions of BSDEJs with Lipschitz generators g that satisfy an additional condition on u−variable (see (A3) therein). Then we demonstrate that the g−expectations, as nonlinear expectations with L p domains under jump filtration, inherit many basic properties from the classic linear expectations and are closely related to axiom-based coherent and convex risk measures (see [4,33,67]) in mathematical finance.…”

Aggregation of Monotonic Bernoullian Archimedean Preferences: Arrovian Impossibility Results

“…Interest in axiomatising such preferences goes back at least to the seminal paper by Ellsberg [6]; since then, various authors have proposed axiomatisations of increasing generality, in particular Gilboa and Schmeidler [12], Föllmer and Schied [8,9] as well as Maccheroni, Marinacci and Rustichini [23]. Recently, even gametheoretic aspects of ambiguity have been studied, for example by Riedel and Sass [24] and Kuzmics [19].…”

Optimal stopping and stochastic control differential games for jump diffusions

“…If we interpret "optimal" in the sense of "risk minimal", then the problem is to find a stopping time τ = τ (ω) which minimizes ρ(X(τ )), where ρ denotes a risk measure. If the risk measure ρ is chosen to be a convex risk measure in the sense of [5] and (or) [4], then it can be given the representation…”