Risk Process with Random Income

Temnov, Grigory

doi:10.1023/b:joth.0000036319.21285.22

Cited by 43 publications

(19 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The particular case of the compound Poisson risk model in the absence of the drift term has also been studied extensively by various authors. For example, ruin probability results can be found in [10,41,48]. More generally, Labbé and Sendova [36] extended the study by showing that the Gerber-Shiu function satisfies a defective renewal equation and providing detailed analysis when the upward jumps follow an Erlang(n) distribution, whereas Albrecher et al [2] considered the Gerber-Shiu function (where the penalty depends on the deficit only) by making assumptions on either upward or downward jumps.…”

Section: Introductionmentioning

confidence: 99%

On a class of stochastic models with two-sided jumps

Cheung

2011

Queueing Syst

View full text Add to dashboard Cite

In this paper a stochastic process involving two-sided jumps and a continuous downward drift is studied. In the context of ruin theory, the model can be interpreted as the surplus process of a business enterprise which is subject to constant expense rate over time along with random gains and losses. On the other hand, such a stochastic process can also be viewed as a queueing system with instantaneous work removals (or negative customers). The key quantity of our interest pertaining to the above model is (a variant of) the Gerber-Shiu expected discounted penalty function (Gerber and Shiu in N. Am. Actuar. J. 2(1):48-72, 1998) from ruin theory context. With the distributions of the jump sizes and their inter-arrival times left arbitrary, the general structure of the Gerber-Shiu function is studied via an underlying ladder height structure and the use of defective renewal equations. The components involved in the defective renewal equations are explicitly identified when the upward jumps follow a combination of exponentials. Applications of the Gerber-Shiu function are illustrated in finding (i) the Laplace transforms of the time of ruin, the time of recovery and the duration of first negative surplus in the ruin context; (ii) the joint Laplace transform 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. Keywords

show abstract

Section: Introductionmentioning

confidence: 99%

On a class of stochastic models with two-sided jumps

Cheung

2011

Queueing Syst

View full text Add to dashboard Cite

show abstract

“…In order to describe the stochastic income, Boucherie et al [3] added a compound Poisson process with positive jumps to the Cramér-Lundberg model. The (non-)ruin probabilities for the risk models with stochastic premiums were studied in Boikov [2] and Temnov [12]. Assuming that the premium process is a Poisson process, Bao [1] studied the Gerber-Shiu function in the compound Poisson risk model.…”

Section: Introductionmentioning

confidence: 99%

On the expected discounted penalty function for a risk model with two classes of claims and random incomes

Xie¹,

Zou²

2014

HJMS

View full text Add to dashboard Cite

In this paper, we consider a risk model with two independent classes of insurance risks and random incomes. We assume that the two independent claim counting processes are, respectively, the Poisson and the Erlang(2) process. When the individual premium sizes are exponentially distributed, the explicit expressions for the Laplace transforms of the expected discounted penalty functions are derived. We prove that the expected discounted penalty functions satisfy some defective renewal equations. By employing an associated compound geometric distribution, the analytic expressions for the solutions of the defective renewal equations are obtained. Assuming that the distributions of premium sizes have rational Laplace transforms, we also give the explicit representations for the Laplace transforms of the expected discounted penalty functions.

show abstract

“…For instance, the continuous-time risk processes with stochastic interest have been studied by many authors; see Paulsen (1993Paulsen ( , 1998, Paulsen and Gjessing (1997), Kalashnikov and Norberg (2002), Bening et al (2004), Cai (2004) and Yuen et al (2004Yuen et al ( , 2006. Temnov (2004) described the premium income by Poisson process and derived an explicit formula for the ruin probability to the corresponding risk process. Motivated by the above findings, this study aims at gaining an insight into the effects of premium incomes on insurance claims under perturbation.…”

Section: Introductionmentioning

confidence: 99%

On the ruin probability for the Cox correlated risk model perturbed by diffusion

Zhang

et al. 2009

Statistics & Probability Letters

View full text Add to dashboard Cite

Risk Process with Random Income

Cited by 43 publications

References 1 publication

On a class of stochastic models with two-sided jumps

On a class of stochastic models with two-sided jumps

On the expected discounted penalty function for a risk model with two classes of claims and random incomes

On the ruin probability for the Cox correlated risk model perturbed by diffusion

Contact Info

Product

Resources

About