ruin related quantities in a class of state-space compound binomial models

The main focus of this paper is to extend the analysis of some ruin related problems to a class of state-space compound binomial risk models for a sequence of independent and identically distributed random variables of interclaim times when the claim occurrences are homogeneous‎. ‎first‎, ‎we obtain the mass function of a defective renewal sequence of random {fn }n≥0 -stopping times‎, ‎using the compound binomial of aggregate claim amount together the net profit condition‎, ‎and compute the infinite time ruin probability with markov property of risk process‎. ‎moreover‎, ‎we derive the distribution of the time to ruin among many random variables associated with ruin using the convolution of claim amount and lagrange's implicit function theorem‎. ‎lastly‎, ‎the theoretical results are illustrated with numerical computations‎.