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

• Published in: Insurance, mathematics & economics Vol. 48; no. 3; pp. 384 - 397
• Main Author: Cheung, Eric C.K.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2011; North Holland Publ. Co; Elsevier; Elsevier Sequoia S.A
• Series: Insurance: Mathematics and Economics
• 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; Surplus-dependent premium rate; Generalized penalty function; Absolute ruin; Gerber–Shiu function; Credit interest; Sparre Andersen model; Threshold dividend strategy
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2011.01.006

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.