Bienaymé-Galton-Watson branching processes subordinated to a continuous time random index are considered. The branching processes are assumed to be critical with finite or infinite offspring variance. The indexing process is assumed to be a renewal one with finite or infinite mean of the...

It is hard to find explicit expressions for the renewal function U(x)=∑n=0∞F∗n(x). Many researchers have made attempts to find suitable approximations for U(x). In this paper we present simple approximations and show that they cover many of the known results.

We obtain limit theorems for the row extrema of a triangular array of zero-modified geometric random variables. Some of this is used to obtain limit theorems for the maximum family size within a generation of a simple branching process with varying geometric offspring laws.

Limiting distributions for the spent and residual life times in a superposition of independent renewal processes are obtained in the case when the interarrival times belong to domains of attraction of stable laws.

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model...

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model...

The point process defines the sequence of maxima . Using time and space scaling it is possible to define different sequences of random time changed extremal processes. The convergence of such sequences to nondegenerate extremal processes is proved in case where the time and space components of...

Recently, new classes of positive and measurable functions, M(ρ) and M(±∞), have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al., 2015, 2016, 2017). Looking for other suitable normalizing functions than logarithm seems quite...