Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend

Abstract In this paper, we model the insurance company’s surplus by a compound Poisson risk model, where process can only be observed at random observation times. It is assumed that insurer observes its level periodically to decide on dividend payments and capital injection interobservation time having an $\operatorname{Erlang}(n)$ Erlang ( n ) distribution. If greater than zero but less line $b_{1} > 0$ b 1 > 0 , shareholders should immediately inject certain amount of bring back $b_{1}$ . larger $b_{2}$ 2 ( $b_{2} b_{1}$ ), any excess over paid out as dividends company. Ruin declared when negative. We derive explicit expressions Gerber–Shiu function, expected discounted injection, payments. Numerical illustrations are also given analyze effect times actuarial quantities.