Strong Limit Theorems for the Risk Process with Stochastic Premiums
2014, v.20, Issue 3, 527-544
General results concerning strong invariance principle for the superposition of random processes are discussed; their applications to investigation of the asymptotic behavior of random sums are presented. As a consequence certain variants of the strong invariance principle for risk processes with stochastic premiums are obtained and used to study the growth rate and fluctuation of such processes under various assumptions on claim size distributions.
Keywords: almost sure convergence,strong invariance principle,superpositionof random processes,random sums,stable process,risk models,law of iterated logarithm