First-Claim Ruin Probability in a Fixed-Claim Insurance Model

Summary

The document poses a classical risk-model question: an insurer receives claims according to a Poisson process, every claim has the same fixed size, and the initial surplus is smaller than one claim. It asks for the probability that ruin occurs at the first claim, given a premium income rate proportional to the claim arrival rate and size.

The setup is a compact exercise in ruin theory, focused on the timing of the first claim rather than the probability of eventual ruin over an unlimited horizon. It provides the model assumptions and premium rate but no solution, derivation, or supporting evidence. Answering it requires considering whether premium income accumulated before the first arrival can raise surplus enough to absorb that claim, using the waiting-time distribution of the Poisson process. The result is relevant to actuarial risk analysis, though it does not describe a trading strategy or market instrument.

Key ideas

• Claim arrivals are modeled as a Poisson process with a positive rate.
• Each claim has a fixed size, and initial surplus is below that size.
• The question concerns ruin at the first claim, accounting for premium income earned before its arrival.
• The document states the model but does not provide a solution.

Tags

# Ruin Probability Question


# Ruin Probability Question












In an insurance company the number of claims are modelled as a Poisson process with rate $\lambda>0$. Assume that the size of all claims is a fixed amount $\alpha>0$, the initial surplus is denoted by $u$, with $0 < u < \alpha$. If the premium income per unit time is $1.73\lambda\alpha$, find the probability that ruin happens at the first claim.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.