A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium

In a general Sparre Andersen risk model with surplus-dependent premium income, the generalization of Gerber–Shiu function proposed by  Cheung et al. (2010a) is studied. A general expression for such Gerber–Shiu function is derived, and it is shown that its determination reduces to the evaluation of...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2011-05, Vol.48 (3), p.384-397
Main Author: Cheung, Eric C.K.
Format: Article
Language:English
Subjects:
Absolute ruin
Actuarial science
Credit
Credit interest
Dividends
Economic models
Generalization
Generalized penalty function
Generalized penalty function Gerber-Shiu function Sparre Andersen model Surplus-dependent premium rate Threshold dividend strategy Credit interest Absolute ruin
Gerber–Shiu function
Income
Modelling
Punishment
Risk
Risk assessment
Risk theory
Sparre Andersen model
Stock returns
Strategic planning
Studies
Surplus-dependent premium rate
Threshold dividend strategy
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Summary:In a general Sparre Andersen risk model with surplus-dependent premium income, the generalization of Gerber–Shiu function proposed by  Cheung et al. (2010a) is studied. A general expression for such Gerber–Shiu function is derived, and it is shown that its determination reduces to the evaluation of a transition function which is independent of the penalty function. Properties of and explicit expressions for such a transition function are derived when the surplus process is subject to (i) constant premium; (ii) a threshold dividend strategy; or (iii) credit interest. Extension of the approach is discussed for an absolute ruin model with debit interest.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2011.01.006