Related papers: Multiportfolio time consistency for set-valued con…
We establish structural properties of optimal stopping problems under time-consistent dynamic (coherent) risk measures, focusing on value function monotonicity and the existence of control limit (threshold) optimal policies. While such…
In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost…
This is a companion paper of [Mixed equilibrium solution of time-inconsistent stochastic LQ problem, arXiv:1802.03032], where general theory has been established to characterize the open-loop equilibrium control, feedback equilibrium…
The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed…
Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim…
The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families…
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the…
We study coherent risk measures which are time-consistent for multiple filtrations. We show that a coherent risk measure is time-consistent for every filtration if and only if it is one of four main types. Furthermore, if the risk measure…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex…
We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which…
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…
This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a…
In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the…
This paper discusses a nonlinear integral equation arising from portfolio selection with a class of time-inconsistent preferences. We propose a unified framework requiring minimal assumptions, such as right-continuity of market coefficients…
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout are the notion of the…