Том 62 ТЕОРИЯ ВЕРОЯТНОСТЕЙ И ЕЕ ПРИМЕНЕНИЯ 2017 2017 г. c PAYANDEH NAJAFABADI A. T.∗∗, BALAKRISHNAN N.∗∗∗ BARMALZAN G.∗, ORDERING RESULTS FOR AGGREGATE CLAIM AMOUNTS FROM TWO HETEROGENEOUS MARSHALL–OLKIN EXTENDED EXPONENTIAL PORTFOLIOS AND THEIR APPLICATIONS IN INSURANCE ANALYSIS В статье обсуждается стохастическое сравнение двух классических процессов капитала страховой компании в случае страхового периода, равного одному году. <...> Consider the classical surplus process U(t) given by U(t) = u+ct− N(t) i=1 ∗Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran; e-mail: ghobad.barmalzan@gmail.com ∗∗Department of Mathematical Sciences, Shahid Beheshti University, G. C. Evin, Tehran, Iran; e-mail: amirtpayandeh@sbu.ac.ir ∗∗∗Department of Mathematics and Statistics, McMaster University, Hamilton, Canada; e-mail: bala@mcmaster.ca Zi, Вып у с к 1 146 Barmalzan G., Payandeh Najafabadi A. T., Balakrishnan N. where u = U(0), c, Zi and N(t) denote an initial surplus, constant premium, random claim and a given counting process, respectively. <...> Under this assumption, the above classical surplus process U(t) for t = 1 can be restated as U(1) = u+c− where the random variable Xλi be made in an insurance period and Ipi i=1 n Ipi Xλi , (1.1) denotes the total of random claims that can denotes a Bernoulli random variable associated withXλi defined as follows: Ipi = 1 whenever the i-th policyholder makes randomclaimXλi and Ipi = 0 whenever he/she does not make a claim. <...> In this work, we then present some stochastic comparisons between two classical surplus processes that can be restated as in (1.1). <...> Since u and c are two constant values, to study any stochastic comparison, we just have to consider n i=1 IpiXλi . <...> Indeed, the random variable Sn(λ,p) =n i=1 IpiXλi is of interest in various fields of probability and statistics. <...> In particular, in actuarial science, it corresponds to the aggregate claim amount in a portfolio of risks. <...> It is <...>