Related papers: Monotonic mean-deviation risk measures
Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables…
In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a…
We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein…
Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information…
We use the martingale method to discuss the relationship between mean-variance (MV) and monotone mean-variance (MMV) portfolio selections. We propose a unified framework to discuss the relationship in general financial markets without any…
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
The investor is interested in the expected return and he is also concerned about the risk and the uncertainty assumed by the investment. One of the most popular concepts used to measure the risk and the uncertainty is the variance and/or…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…
We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…
We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable…
We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions…
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with…
We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of $\mathcal{P}$-quasisure bounded random variables, where $\mathcal{P}$ is a (possibly non-dominated) class of probability…