Related papers: On the Separability of Vector-Valued Risk Measures

The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In…

In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the…

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the context of bounded financial positions, the class of…

We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…

Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness,…

Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…

This seemed impossible to use a theoretically adequate but too sophisticated risk measure called non-ruin capital, whence its widespread (including regulatory documents) replacement with an inadequate, but simple risk measure called…

We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail…

Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious…

We present a general framework for measuring the liquidity risk. The theoretical framework defines a class of risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement…

The vector cost bimatrix game is a method for multi-objective decision making that enables autonomous robotic systems to optimize for multiple goals at once while avoiding worst-case scenarios in neglected objectives. We expand this…

We propose a convex formulation for a trading system with the Conditional Value-at-Risk as a risk-adjusted performance measure under the notion of Direct Reinforcement Learning. Due to convexity, the proposed approach can uncover a…

Ensuring that classifiers are non-discriminatory or fair with respect to a sensitive feature (e.g., race or gender) is a topical problem. Progress in this task requires fixing a definition of fairness, and there have been several proposals…

This article proposes a new index for quantifying the degree of dependence between random vectors. The index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent. Unlike mere uncorrelatedness,…

Prediction markets are well-studied in the case where predictions are probabilities or expectations of future random variables. In 2008, Lambert, et al. proposed a generalization, which we call "scoring rule markets" (SRMs), in which…

The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion…

The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for…

Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a…

Probabilistic risk aversion, defined through quasi-convexity in probabilistic mixtures, is a common useful property in decision analysis. We study a general class of non-monotone mappings, called the generalized rank-dependent functions,…

CVaR (Conditional Value at Risk) is a risk metric widely used in finance. However, dynamically optimizing CVaR is difficult since it is not a standard Markov decision process (MDP) and the principle of dynamic programming fails. In this…