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Hunger for Bonus

Definition

Hunger for bonus is a policyholder's incentive not to report a small covered loss when reporting would increase expected future premiums by more than the current reimbursement. It is a behavioural response to a bonus-malus experience-rating rule.

Interpretation

The reported claim record can understate accident experience. The course treats this response as a form of moral hazard (a change in the insured's behaviour caused by the insurance contract itself); it changes the observation process on which rating relies.

Reimbursement line against a flat 120 of extra expected discounted premiums: below the crossing at 120 the loss is not reported, above it reporting pays; the cases 80 and 200 are marked.

The figure draws the Examples comparison. Reporting brings in the reimbursement (red line) but costs the 120 of extra expected discounted future premiums (dashed blue). The lines cross at 120, so a policyholder minimizing expected monetary cost keeps the loss with reimbursement 80 unreported and reports the one with reimbursement 200. The crossing acts as a private reporting threshold, although the contract itself need not have a deductible.

The bonus-malus rule determines how reporting changes the policyholder's current class and subsequent premiums. This decision compares the two future premium streams starting from the current class; it does not require the portfolio to be in its stationary bonus-malus distribution.

Key Results

  • A simple decision compares the current payment with the present value of extra future premiums caused by reporting.
  • The relevant future difference depends on current level, transition rules, time horizon and discounting.
  • Observed claim frequency can differ from accident frequency.
  • A reporting threshold need not equal a contractual deductible.

Examples

If reimbursement would be 80 but reporting increases expected discounted future premiums by 120, a policyholder minimizing expected monetary cost prefers not to report. For reimbursement 200, the same comparison favours reporting.

Prerequisites

Sources

Aliases: claim suppression incentive, bonus-malus reporting threshold, bonus hunger Keywords: not reporting small claims, moral hazard, discounted future premiums, reported versus accident frequency

Last updated: 16 October 2026 22:28