Determination of Risk Pricing Measures from Market Prices of Risk

A new insurance provider or a regulatory agency may be interested in determining a risk measure consistent with observed market prices of a collection of risks. Using a relationship between distorted coherent risk measures and spectral risk measures, we provide a method for reconstruction distortion functions from the observed prices of risk. The technique is based on an appropriate application of the method on maximum entropy in the mean.

Comprehensive entropy weight observability-controllability risk analysis and its application to water resource decision-making

Decision making for water resource planning is often related to social, economic and environmental factors. There are various methods for making decisions about water resource planning alternatives and measures with various shortcomings. A comprehensive entropy weight observability-controllability risk analysis approach is presented in this study. Computing methods for entropy weight (EW) and subjective weight (SW) are put forward based on information entropy theory and experimental psychology principles, respectively. Comprehensive weight (CW) consisting of EW and SW is determined. The values of observability-controllability risk (Roc) and gain by comparison (Gbc) are obtained based on the CWs. The quantitative analysis of alternatives and measures is achieved based on Roc and Gbc. A case study on selection of water resource planning alternatives and measures in the Yellow River Basin, China, was performed. Results demonstrate that the approach presented in this study can achieve optimal decision-making results

Extreme Entropy Machines: Robust information theoretic classification

Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information theoretic way by investigating applicability of entropy measures as a classification model objective function. We focus on quadratic Renyi's entropy and connected Cauchy-Schwarz Divergence which leads to the construction of Extreme Entropy Machines (EEM). The main contribution of this paper is proposing a model based on the information theoretic concepts which on the one hand shows new, entropic perspective on known linear classifiers and on the other leads to a construction of very robust method competetitive with the state of the art non-information theoretic ones (including Support Vector Machines and Extreme Learning Machines). Evaluation on numerous problems spanning from small, simple ones from UCI repository to the large (hundreads of thousands of samples) extremely unbalanced (up to 100:1 classes' ratios) datasets shows wide applicability of the EEM in real life problems and that it scales well

On a relationship between distorted and spectral risk measures

We study the relationship between two widely used risk measures, the spectral measures and the distortion risk measures. In both cases, the risk measure can be thought of as a re-weighting of some initial distribution. We prove that spectral risk measures are equivalent to distorted risk pricing measures, or equivalently, spectral risk functions are related to distortion functions. Besides that we prove that distorted measures are absolutely continuous with respect to the original measure. This allows us to find a link between the risk measures based on relative entropy and spectral risk measures or measures based on distortion risk function

Compositional closure for Bayes Risk in probabilistic noninterference

We give a sequential model for noninterference security including probability (but not demonic choice), thus supporting reasoning about the likelihood that high-security values might be revealed by observations of low-security activity. Our novel methodological contribution is the definition of a refinement order and its use to compare security measures between specifications and (their supposed) implementations. This contrasts with the more common practice of evaluating the security of individual programs in isolation. The appropriateness of our model and order is supported by our showing that our refinement order is the greatest compositional relation --the compositional closure-- with respect to our semantics and an "elementary" order based on Bayes Risk --- a security measure already in widespread use. We also relate refinement to other measures such as Shannon Entropy. By applying the approach to a non-trivial example, the anonymous-majority Three-Judges protocol, we demonstrate by example that correctness arguments can be simplified by the sort of layered developments --through levels of increasing detail-- that are allowed and encouraged by compositional semantics

Income Inequality Measures and Statistical Properties of Weighted Burr-type and Related Distributions

In this thesis, tail conditional expectation (TCE) in risk analysis, an important measure for right-tail risk, is presented. This value is generally based on the quantile of the loss distribution. Explicit formulas of several tail conditional expectations and inequality measures for Dagum-type models are derived. In addition, a new class of weighted Burr-III (WBIII) distribution is presented. The statistical properties of this distribution including hazard and reverse hazard functions, moments, coefficient of variation, skewness, and kurtosis, inequality measures, entropy are derived. Also, Fisher information and maximum likelihood estimates of the model parameters are obtained

Entropy and systemic risk measures

The aim of this paper is the construction of an early warning indicator for systemic risk using entropy measures. The analysis is based on the cross-sectional distribution of marginal systemic risk measures such as Marginal Expected Shortfall, Delta CoVaR and network connectedness. These measures are conceived at a single institution for the financial industry in the Euro area. Entropy indicators show forecasting abilities in predicting banking crises revealing to be an effective tool as early warning indicator

Entropy-Based Financial Asset Pricing

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return - entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behaviour of the beta along with entropy.Comment: 21 pages, 6 figures, 3 tables and 4 supporting file