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Total duration of negative surplus for the dual model
Author(s) -
Song Min,
Wu Rong,
Zhang Xin
Publication year - 2008
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.733
Subject(s) - laplace transform , zero (linguistics) , mathematics , duration (music) , dual (grammatical number) , sequence (biology) , exponential function , jump , exponential distribution , surplus value , mathematical economics , economics , laplace distribution , econometrics , statistics , mathematical analysis , physics , art , philosophy , linguistics , literature , quantum mechanics , biology , politics , political science , acoustics , law , capitalism , genetics
In the dual model, we allow the surplus process to continue if the surplus falls below zero. By introducing the renewal measure of the defective renewal sequence constituted by the zero points of the surplus process, we obtain the probability of hitting the zero point. Further, we derive formulae for the Laplace transform, expectation and variance of total duration of negative surplus and present some examples with an exponential individual jump amount distribution. Copyright © 2008 John Wiley & Sons, Ltd.