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Optimal Reinsurance under Distortion Risk Measures
Distortion risk measure expected premium principle the optimal reinsurance strategy VaR TVaR
2016/1/25
In this paper, we discuss the optimal reinsurance strategy of minimizing the in-surer’s risk under the distortion risk measure. We assume that reinsurance premium is determined by the expected premium...
Optimal Reinsurance under Distortion Risk Measures
Distortion risk measure expected premium principle the optimal reinsurance strategy VaR TVaR
2016/1/20
In this paper, we discuss the optimal reinsurance strategy of minimizing the in-surer’s risk under the distortion risk measure. We assume that reinsurance premium is determined by the expected premium...
Statistical equilibrium measures in micromagnetics
Equilibrium statistical theory ferromagnetic materials rotate fluctuations
2014/12/29
We derive an equilibrium statistical theory for the macroscopic description of a ferromagnetic material at positive finite temperatures. Our formulation describes the most-probable equilibrium macrost...
Measures of serial extremal dependence and their estimation
Measures serial extremal dependence their estimation
2013/4/28
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent conc...
Spectral Risk Measures, With Adaptions For Stochastic Optimization
Spectral Risk Measures Adaptions Stochastic Optimization
2012/11/22
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to qua...
On the Weakenesses of Correlation Measures used for Search Engines' Results (Unsupervised Comparison of Search Engine Rankings)
Search Engines Correlation Measures Search Engine Rankings
2011/7/19
The correlation of the result lists provided by search engines is fundamental and it has deep and multidisciplinary ramifications. Here, we present automatic and unsupervised methods to assess whether...
Coupled risk measures and their empirical estimation when losses follow heavy-tailed distributions
Risk measure Heavy-tailed distribution Distortion risk measure Weighted risk measure Proportional hazards transform Conditional tail expectation Premium calculation principle Index of economic inequality Statistical inference
2011/6/20
Considerable literature has been devoted to developing statistical
inferential results for risk measures, especially for those that are
of the form of L-functionals. However, practical and theoretic...
PAC learnability under non-atomic measures: a problem by Vidyasagar
PAC learnability non-atomic measures learning rule uniform GlivenkoCantelli classes Martin’s Axiom VC dimension modulo countable sets fat shattering dimension modulo countable sets
2011/6/20
In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept
class C under the family of all non-atomic (diffuse) measures on the domain
. The uniform Gliv...
Transportation inequalities: From Poisson to Gibbs measures
Gibbs measures Poisson point processes transportation inequalities
2011/3/21
We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality...
Estimating the scaling function of multifractal measures and multifractal random walks using ratios
namely mutiplicative cascades structure function
2011/3/24
In this paper we prove central limit theorems for bias reduced estimators of the structure function of several multifractal processes, namely mutiplicative cascades, multifractal random measures, mult...
Optimal measures and transition kernels
Optimization and Control (math.OC) Computational Complexity (cs.CC) Information Theory (cs.IT) Mathematical Physics (math-ph) Functional Analysis (math.FA) Machine Learning (stat.ML)
2010/12/17
We study positive measures that are solutions to an abstract optimisation problem, which is a generalisation of a classical variational problem with a constraint on information of a Kullback-Leibler t...
Information theoretic interpretation of frequency domain connectivity measures
Statistics Theory (math.ST) Neurons and Cognition (q-bio.NC)
2010/12/17
To provide adequate multivariate measures of information flow between neural structures, modified expressions of Partial Directed Coherence (PDC) and Directed Transfer Function (DTF), two popular mult...
Mixed models for longitudinal left-censored repeated measures
Mixed model Repeated measures Left-censoring SAS proc NLMIXED HIV infection
2010/4/29
Longitudinal studies could be complicated by left-censored repeated measures. For example, in Human Immunodeficiency Virus infection, there is a detection limit of the assay used to quantify the plasm...
Zipf's law and log-normal distributions in measures of scientific output across fields and institutions：40 years of Slovenia's research as an example
Zipf’s law citation distribution g-index h-index ranking
2010/3/11
Slovenia’s Current Research Information System (SICRIS) currently hosts 86,443 publications with citation data from 8,359 researchers working on the whole plethora of social and natural sciences from ...
Universality,Characteristic Kernels and RKHS Embedding of Measures
Kernel methods Characteristic kernels Hilbert space embeddings Universalkernels Translation invariant kernels Radial kernels
2010/3/11
A Hilbert space embedding for probability measures has recently been proposed, wherein
any probability measure is represented as a mean element in a reproducing kernel Hilbert
space (RKHS). Such an ...