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Estimations and asymptotic behaviors of coherent entropic risk measure for sums of random variables
Institution:1. Department of Epidemiology and Biostatistics, School of Public Health, Indiana University Bloomington, 1025 E. 7th street, PH C104, Bloomington, IN, 47405, USA;2. Department of Epidemiology and Biostatistics, University of Georgia, Athens, GA 30602, USA;3. Department of Statistical Science, Southern Methodist University, 3225 Daniel Avenue, PO Box 750332, Dallas, TX 75275-0332, USA;1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, China;2. School of Economics and Management, Southeast University, Nanjing, 210096, China;3. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania;4. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, Vilnius LT-08663, Lithuania;1. Université de Rouen, LITIS EA 4108, Avenue de l’Université, BP 12, 76801 Saint-Étienne-du-Rouvray, France;2. Rutgers University, Department of Statistics, 561 Hill Center, Busch Campus, Piscataway, NJ 08854-8019, USA;1. Clausthal University of Technology, Department of Applied Stochastics and Operations Research, 38678 Clausthal-Zellerfeld, Germany;2. University of Derby, School of Computing and Mathematics, Derby, DE22 1GB, UK
Abstract:In this article, we provide an estimation and several asymptotic behaviors for the coherent entropic risk measure of compound Poisson process. We also establish an estimation for the coherent entropic risk measure of sum of i.i.d. random variables in virtue of Log-Sobolev inequality. As an application, we provide two deviation estimations of the tail probability for compound Poisson process. Finally, several simulation results are given to support our results.
Keywords:Convex entropic risk measure  Coherent entropic risk measure  Compound Poisson process  Asymptotic behaviors
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