Related papers: Decomposability and time consistency of risk avers…
In this paper we provide a flexible framework allowing for a unified study of time consistency of risk measures and performance measures (also known as acceptability indices). The proposed framework not only integrates existing forms of…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which multiple risk-averse agents choose their decisions in such a way to minimize their individual accumulated…
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain…
We develop an approach to time-consistent risk evaluation of continuous-time processes in Markov systems. Our analysis is based on dual representation of coherent risk measures, differentiability concepts for multivalued mappings, and a…
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional…
Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and of storage, make their management a delicate…
This paper shows how the theory of dynamic risk measures provides viscosity solutions to a family of second-order parabolic partial differential equations, even in the degenerate case. First, motivated by the martingale problem approach of…
We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a…
Equivalent characterizations of multiportfolio time consistency are deduced for closed convex and coherent set-valued risk measures on $L^p(\Omega,\mathcal F, P; R^d)$ with image space in the power set of $L^p(\Omega,\mathcal F_t,P;R^d)$.…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
This paper is devoted to solving a time-inconsistent risk-sensitive control problem with parameter $\e$ and its limit case ($\e\rightarrow0^+$) for countable-stated Markov decision processes (MDPs for short). Since the cost functional is…
Multi-period measures of risk account for the path that the value of an investment portfolio takes. In the context of probabilistic risk measures, the focus has traditionally been on the magnitude of investment loss and not on the dimension…
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of…
This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time.…
This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of…
We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by $g$-evaluations. For such problems, we…
In this paper, we deal with risk evaluation and risk-averse optimization of complex distributed systems with general risk functionals. We postulate a novel set of axioms for the functionals evaluating the total risk of the system. We derive…
For optimal stopping problems with time-inconsistent preference, we measure the inherent level of time-inconsistency by taking the time needed to turn the naive strategies into the sophisticated ones. In particular, when in a repeated…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…