Bi-seasonal discrete time risk model with income rate two

TL;DR

This paper analyzes the ultimate survival probability in a bi-seasonal discrete time risk model with an income rate of two, extending previous work with an income rate of one, and provides numerical illustrations and conjectures.

Contribution

It introduces an approximate method for calculating survival probabilities in a bi-seasonal risk model with income rate two, expanding prior models with income rate one.

Findings

Numerical calculations illustrate theoretical results.

Conjectures on recurrent determinants non-vanishing are proposed.

Extended analysis of risk models with bi-seasonal income rates.

Abstract

This paper proceeds an approximate calculation of ultimate time survival probability for bi-seasonal discrete time risk model when premium rate equals two. The same model with income rate equal to one was investigated in 2014 by Damarackas and \v{S}iaulys. In general, discrete time and related risk models deal with possibility for a certain version of random walk to hit a certain threshold at least once in time. In this research, the mentioned threshold is the line $u+2t$ and random walk consists from two interchangeably occurring independent but not necessarily identically distributed random variables. Most of proved theoretical statements are illustrated via numerical calculations. Also, there are raised a couple of conjectures on a certain recurrent determinants non-vanishing.