Assume that the random future evolution of values is modelled in continuous time. Then, a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. In this paper we study coherent and convex monetary risk measures on the space of all càdlàg processes that...

Abstract We characterize when a convex risk measure associated to a law-invariant acceptance set in L ∞ can be extended to L p , $1\le p<\infty $ , preserving finiteness and continuity . This problem is strongly connected to the statistical robustness of the corresponding risk measures....

Abstract Let 𝒳 be a subset of L^{1} that contains the space of simple random variables ℒ and \rho\colon\mathcal{X}\to(-\infty,\infty] a dilatation monotone functional with the Fatou property. In this note, we show that 𝜌 extends uniquely to a \sigma(L^{1},\mathcal{L}) lower...

Summary Robust utility functionals arise as numerical representations of investor preferences, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In this paper, we study the duality theory for the problem of maximizing the...

SUMMARY We give an explicit PDE characterization for the solution of a robust utility maximization problem in an incomplete market model, whose volatility, interest rate process, and long-term trend are driven by an external stochastic factor process. The robust utility functional is defined in...

Summary Using a backward stochastic differential equation (BSDE) approach in a Brownian motion setting, we determine in an incomplete market an initial price Y 0 for a non-attainable claim ξ ∈ L p , 1 p ∞, that takes the hedging risk into account. Y 0 is chosen to be the best price such...

Abstract We deal with the problem of the practical use of Haezendonck risk measures (see Haezendonck and Goovaerts [8], Goovaerts et al. [7], Bellini and Rosazza Gianin [4]) in portfolio optimization. We first analyze the properties of the natural estimators of Haezendonck risk measures by means...

We investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock price follows specific processes, spectral risk becomes...