Analysis of risk models using a level crossing technique

Brill, Percy H.; Yu, Kaiqi

doi:10.1016/j.insmatheco.2011.05.005

Cited by 4 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, differently from Brill and Yu (2011), we obtain the expected number of the up-crossing of a level, and using this, we drive the distribution of the stationary surplus level. Brill and Yu (2011) also adopted the level-crossing argument to obtain the distribution of the stationary surplus level, while they obtained the renewal type equation (or Volterra integral equation) for the p.d.f. of the stationary surplus level.…”

Section: Resultsmentioning

confidence: 99%

“…Numerical example: Suppose that the claim size is exponentially distributed with rate µ = 6.0 and c = 2.05 for the comparison with the numerical results of Brill and Yu (2011). We assume that the arrival rates are λ = 11.8 and 12.29.…”

Section: Exponentially Distributed Claim Sizesmentioning

confidence: 99%

“…The modified risk model has been introduced and studied by Brill and Yu (2011) and Jeong, Lim, and Lee (2009). Brill and Yu (2011) derived a renewal type equation for the stationary distribution of the surplus process and obtain the exact form of the stationary distribution when the claim sizes are exponentially distributed.…”

Section: Introductionmentioning

confidence: 99%

“…Brill and Yu (2011) derived a renewal type equation for the stationary distribution of the surplus process and obtain the exact form of the stationary distribution when the claim sizes are exponentially distributed. Under a certain cost structure, Jeong et al (2009) obtained the long-run average cost as a function of M and a, and illustrated an example how to find the optimal values of M and a which minimize the long-run average cost.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stationary distribution of the surplus in a risk model with dividends and reinvestments

Kim

Lee

2015

Journal of the Korean Statistical Society

View full text Add to dashboard Cite

a b s t r a c tA continuous time risk model with dividends and reinvestments is considered. We obtain an explicit formula of the stationary distribution of the surplus and the expected time to ruin after a reinvestment by adopting the level crossing argument. We also propose a scheme to approximate the stationary distribution of the surplus. As an example, we consider the case when the claims are exponentially distributed, Erlang distributed, and generalized hyperexponentially distributed.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Exponentially Distributed Claim Sizesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stationary distribution of the surplus in a risk model with dividends and reinvestments

Kim

Lee

2015

Journal of the Korean Statistical Society

View full text Add to dashboard Cite

show abstract

“…Level-crossing methods also lead to the time-t quantities (Section 3.1.2). The new method connects the analysis of the time-t quantities with the analyses of queues having bounded wait, inventories, dams, replacement models, and actuarial ruin models (Brill and Yu [15]). It provides a completely different perspective of the time-t quantities and suggests new avenues of research.…”

Section: Introductionmentioning

confidence: 99%

Alternative Analysis of Finite-Time Probability Distributions of Renewal Theory

Brill¹

2014

Prob. Eng. Inf. Sci.

Self Cite

View full text Add to dashboard Cite

We introduce a level-crossing analysis of the finite time-t probability distributions of the excess life, age, total life, and related quantities of renewal processes. The technique embeds the renewal process as one cycle of a regenerative process with a barrier at level t, whose limiting probability density function leads directly to the time-t quantities. The new method connects the analysis of renewal processes with the analysis of a large class of stochastic models of Operations Research. Examples are given.

show abstract

Note on the service time in an M/G/1 queue with bounded workload

Brill

2015

Statistics & Probability Letters

Self Cite

View full text Add to dashboard Cite

Analysis of risk models using a level crossing technique

Cited by 4 publications

References 29 publications

Stationary distribution of the surplus in a risk model with dividends and reinvestments

Stationary distribution of the surplus in a risk model with dividends and reinvestments

Alternative Analysis of Finite-Time Probability Distributions of Renewal Theory

Note on the service time in an M/G/1 queue with bounded workload

Contact Info

Product

Resources

About