Unified approach for solving exit problems for additive-increase and multiplicative-decrease processes

Abstract We analyse an additive-increase and multiplicative-decrease (also known as growth–collapse) process that grows linearly in time that, at Poisson epochs, experiences downward jumps are (deterministically) proportional to its present position. For this process, also for reflected versions, we consider one- two-sided exit problems concern the identification of laws times from fixed intervals half-lines. All proofs based on a unified first-step analysis approach first jump epoch, which allows us give explicit, yet involved, formulas their Laplace transforms. eight transforms can be described terms two so-called scale functions associated with upward one-sided time. other obtained above by taking limits, derivatives, integrals, combinations these.