Related papers: Multi-asset return risk measures
In several applications such as clinical trials and financial portfolio optimization, the expected value (or the average reward) does not satisfactorily capture the merits of a drug or a portfolio. In such applications, risk plays a crucial…
The conditional mean risk-sharing (CMRS) rule is an important tool for distributing aggregate losses across individual risks, but its implementation in continuous multivariate models typically requires complicated multidimensional…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit, more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex…
Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i)…
Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…
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…
A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…
In contrast to the popular Cox model which presents a multiplicative covariate effect specification on the time to event hazards, the semiparametric additive risks model (ARM) offers an attractive additive specification, allowing for direct…
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…
Recently, Castagnoli et al. (2021) introduce the class of star-shaped risk measures as a generalization of convex and coherent ones, proving that there is a representation as the pointwise minimum of some family composed by convex risk…
Markov games (MGs) and multi-agent reinforcement learning (MARL) are studied to model decision making in multi-agent systems. Traditionally, the objective in MG and MARL has been risk-neutral, i.e., agents are assumed to optimize a…
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…
We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a…
We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel…
Geometrically convex functions constitute an interesting class of functions obtained by replacing the arithmetic mean with the geometric mean in the definition of convexity. As recently suggested, geometric convexity may be a sensible…
We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the…
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…
This paper investigates how to measure common market risk factors using newly proposed Panel Quantile Regression Model for Returns. By exploring the fact that volatility crosses all quantiles of the return distribution and using penalized…
We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution…