Related papers: Spectral Risk Measures and the Choice of Risk Aver…
Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found…
Agents' learning from feedback shapes economic outcomes, and many economic decision-makers today employ learning algorithms to make consequential choices. This note shows that a widely used learning algorithm, $\varepsilon$-Greedy, exhibits…
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…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
We review the recently introduced concept of variety of a financial portfolio and we sketch its importance for risk control purposes. The empirical behaviour of variety, correlation, exceedance correlation and asymmetry of the probability…
We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. We show that for non-expected utility maximizers choosing between multivariate prospects, aversion to multivariate mean preserving increases in risk is…
The debate of what quantitative risk measure to choose in practice has mainly focused on the dichotomy between Value at Risk (VaR) -- a quantile -- and Expected Shortfall (ES) -- a tail expectation. Range Value at Risk (RVaR) is a natural…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
How should well-being be prioritised in society, and what trade-offs are people willing to make between fairness and personal well-being? We investigate these questions using a stated preference experiment with a nationally representative…
We consider reinforcement learning with performance evaluated by a dynamic risk measure. We construct a projected risk-averse dynamic programming equation and study its properties. Then we propose risk-averse counterparts of the methods of…
The aim of this study is to present proofs for new theorems. Basic thoughts of new definitions emerge from the decision-making under uncertainty in economics and finance. Shape of the certain utility curve is central to standard definitions…
We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our…
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…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
Informally, a risk measure is said to be elicitable if there exists a suitable scoring function such that minimizing its expected value recovers the risk measure. In this paper, we analyze the elicitability properties of the class of return…
A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with…
We extend well-known comparative results under expected utility to models of non-expected utility by providing novel conditions on local utility functions. We illustrate how our results parallel, and are distinct from, existing results for…
We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…
Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This…