This report proposes a discrete-time NCD risk model that incorporates the well-known No Claim Discount (NCD) system in general insurance industry. Under the system, the level of premium that the insurer will receive in a given time period depends on the amount of claims the insurer paid in previous time period. For simplicity, only two levels of premium are considered. Recursive formulae are derived for ultimate ruin probabilities, and explicit expressions are also obtained for certain cases. At last, the impact of the NCD system on ruin probabilities is examined through numerical examples.
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