Ruin probability for inhomogeneous compound discrete-time renewal risk model

In the beginning of the master thesis, the conditions are considered under which distribution of random sum ξ1+ξ2+. . .+ξη belongs to the class L intersection with D. Here {ξ1, ξ2, . . .} is a sequence of independent but not necessarily identically distributed non-negative random variables (r.v), while η is non-negative, non-degenerate at zero, integer valued and independent of {ξ1, ξ2, . . .} r.v. In the second part of the thesis, after all necessary conditions are analyzed, the asymptotic formula is considered for the finite time ruin probability for Inhomogeneous Compound Discrete-Time Renewal Risk model. Such model is defined by the formula: ˆU(t) = u + ct –sum_{k=1}to{t}sum_{i=1}to{η_k}(ξi )^(k), t in N where u >= 0 is initial risk reserve, o c > 0 premium intensity. A sequence of r.v. {(ξ1)^(k), (ξ2)^(k), . . .}k=1 to infinity describes claims sizes at moment k. We suppose that {(ξ1)^(k), (ξ2)^(k), . . .}k=1 to infinity are copies of independent sequence of r.v. {ξ1, ξ2, . . .} with distribution functions {F 1 , F 2 , . . .}. Non-negative, non-degenerate at zero and integer-valued r.v. η_k is the number of claims within time interval (k − 1, k] with distribution function Fη. In addition, we suppose that r.v. η1, η2, . . . and (ξ1)^(1) , (ξ2)^(1), . . . , (ξ1)^(2) , (ξ2)^(2),. . . are independent. Finally, we apply obtained asymptotic formula for more specific risk renewal model, where r.v. η has a bounded support and F_ξi belong to class L intersection with D for each i = 1, 2, . .