an:06000228
Zbl 1235.60126
Cheung, Eric C. K.
On a class of stochastic models with two-sided jumps
EN
Queueing Syst. 69, No. 1, 1-28 (2011).
00287336
2011
j
60K25 60K15 90B22 91B30 60J75
dual risk model; two-sided jumps; \(GI/G/1\) queue; negative customers; Gerber-Shiu function; defective renewal equation; time of ruin; time of recovery; busy period; idle period
The paper studies the Gerber-Shiu function in a stochastic model involving two-sided jumps and a continuous downward drift. With arbitrary distributions of jump sizes and inter-arrival times, the general structure of the Gerber-Shiu function is studied via an underlying ladder height structure and the use of defective renewal equations. Applications of the Gerber-Shiu function are illustrated in finding (i) the Laplace transforms of the time of the ruin, the time of recovery and the duration of first negative surplus in the ruin context; (ii) the joint Laplace transforms of the busy period and the subsequent idle period in the queueing context; and (iii) the expected total discounted reward for a continuous payment stream payable during idle periods in a queue.
Oleg K. Zakusilo (Ky??v)