UPPER BOUNDS FOR RUIN PROBABILITY IN A CONTROLLED GENERAL RISK PROCESS WITH RATE OF INTEREST IS A FIRST - ORDER - Quang Phung Duy, Thinh Nguyen Huu, Chien Doan Quyet, Nhat Nguyen Hong (Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021)
In this paper, we study a controlled general risk process where claim is homogeneous Markov chain and rate of interest is a first-order autoregressive process. We assume that claim is homogeneous Markov chain, take a countable number of nonnegative values and rate of interest is a sequence of non-negative random variables what it satifies a first-order autoregressive process. Generalized Lundberg inequalities for ruin probability of this process are derived by the Martingale approach.