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We construct a discrete-time ruin model with general premium rate and dependent setting, where the time between two occurrences depends on the previous claim size. The generating function and defective renewal equation satisfied by the Gerber-Shiu expected discounted penalty function are derived by using the roots of a generalized Lundberg’s equation. Explicit expressions for the Gerber-Shiu function are obtained with discrete Km$K_{m}$-family claim sizes and geometric thresholds. Numerical illustration is then examined.

A discrete-time ruin model with dependence between interclaim arrivals and claim sizes