Discrete‐Time Risk Model With Time‐Varying Premiums: Analysis of Ruin Probabilities

ABSTRACT Our paper explores a discrete‐time risk model with time‐varying premiums, investigating two types of correlated claims: main claims and by‐claims. Settlement of the by‐claims can be delayed for up to two time periods, representing real‐world insurance practices. We examine a premium principle based on reported claims, using recursively computable finite‐time ruin probabilities to evaluate the performance of time‐varying premiums. Our findings suggest that, under specific assumptions, a higher probability of by‐claim settlement delays leads to lower ruin probabilities. Moreover, a stronger correlation between main claims and their associated by‐claims results in higher ruin probabilities.