Related papers: Convex Risk Measures based on Divergence
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is…
Measuring model risk is required by regulators on financial and insurance markets. We separate model risk into parameter estimation risk and model specification risk, and we propose expected shortfall type model risk measures applied to…
The convex analytic method has proved to be a very versatile method for the study of infinite horizon average cost optimal stochastic control problems. In this paper, we revisit the convex analytic method and make three primary…
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss…
We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
This paper applies risk analysis to medical problems, through the properties of nonlinear responses (convex or concave). It shows 1) necessary relations between the nonlinearity of dose-response and the statistical properties of the…
Environmental variables that fluctuate randomly and dynamically over time, such as water quality indices, are considered to be stochastic. They exhibit sub-exponential memory structures that should be accounted for in their modeling and…
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…
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 studies an optimal insurance contracting problem in which the preferences of the decision maker given by the sum of the expected loss and a convex, increasing function of a deviation measure. As for the deviation measure, our…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that…
Constrained optimization provides a common framework for dealing with conflicting objectives in reinforcement learning (RL). In most of these settings, the objectives (and constraints) are expressed though the expected accumulated reward.…
In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such…
Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this…
Reliable, risk-averse design of complex engineering systems with optimized performance requires dealing with uncertainties. A conventional approach is to add safety margins to a design that was obtained from deterministic optimization.…