Analysis of the Gerber–Shiu function and dividend barrier problems for a risk process with two classes of claims

Chadjiconstantinidis, Stathis; Papaioannou, Apostolos D.

doi:10.1016/j.insmatheco.2009.10.003

Cited by 7 publications

(10 citation statements)

References 22 publications

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“…we conclude that there is a root z = r ∈ (vq 1 q 2 , v ] to Equation (14). Moreover, it is known from the safety loading condition Equation 3that…”

Section: The Generating Function Of the Expected Discounted Penalty Fmentioning

confidence: 64%

“…It is easy to verify that (zĝ(z)) > 0 and (zĝ(z)) > 0, which implies that zĝ(z) is an increasing convex function. Hence, Equation (14) has at most two roots. By noting that…”

Section: The Generating Function Of the Expected Discounted Penalty Fmentioning

confidence: 99%

“…Meanwhile, attention has also been paid to risk models whose aggregate claim process is a book of insurance business. For instance, see [10][11][12][13][14][15], among many others. In the case of two classes of business, Wu and Yuen [16] consider an interaction risk model with delayed claims and derive a recursive equation for the finite time survival probabilities.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On a Discrete Interaction Risk Model with Delayed Claims

Zhang

2015

JRFM

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We study a discrete-time interaction risk model with delayed claims within the framework of the compound binomial model. Using the technique of generating functions, we derive both a recursive formula and a defective renewal equation for the expected discounted penalty function. As applications, the probabilities of ruin and the joint distributions of the surplus one period to ruin and the deficit at ruin are investigated. Numerical illustrations are also given.

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“…we conclude that there is a root z = r ∈ (vq 1 q 2 , v ] to Equation (14). Moreover, it is known from the safety loading condition Equation 3that…”

Section: The Generating Function Of the Expected Discounted Penalty Fmentioning

confidence: 64%

“…It is easy to verify that (zĝ(z)) > 0 and (zĝ(z)) > 0, which implies that zĝ(z) is an increasing convex function. Hence, Equation (14) has at most two roots. By noting that…”

Section: The Generating Function Of the Expected Discounted Penalty Fmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On a Discrete Interaction Risk Model with Delayed Claims

Zhang

2015

JRFM

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“…The authors derived an integro-differential equation system for the Gerber-Shiu functions, and obtained their Laplace transforms when the corresponding Lundberg equation has distinct roots. Chadjiconstantinidis and Papaioannou [4] studied a risk model with two independent classes of insurance risks in the presence of a constant dividend barrier. A system of integro-differential equations with certain boundary conditions for the Gerber-Shiu function was derived and solved.…”

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

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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.

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“…A system of integro-differential equations for the expected discounted penalty function was derived and solved. For more related references on two classes of risk processes problem, the reader may consult the following publications and references therein, Yuen et al (2002), Li and Garrido (2005), Chadjiconstantinidis and Papaioannou (2009), etc. Under the above risk models, premiums are assumed to be received by insurance companies at a constant rate over time.…”

Section: Introductionmentioning

confidence: 99%

Analysis of ruin measures for two classes of risk processes with stochastic income

Jiang¹

2014

HJMS

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In this paper, we consider the ruin measures for two classes of risk processes. We assume that the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Historically, it has been assumed that the premium size is a constant. In this contribution, the premium income arrival process is a Poisson process. In this framework, both the integro-differential equation and the Laplace transform for the expected discounted penalty function are established. Explicit expressions for the expected discounted penalty function are derived when the claim amount distributions belong to the rational family. Finally, Numerical examples are considered.

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Analysis of the Gerber–Shiu function and dividend barrier problems for a risk process with two classes of claims

Cited by 7 publications

References 22 publications

On a Discrete Interaction Risk Model with Delayed Claims

On a Discrete Interaction Risk Model with Delayed Claims

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

Analysis of ruin measures for two classes of risk processes with stochastic income

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