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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

In the classical compound Poisson surplus model, claims arrive at Poisson rate λ, individual claims are exponential with mean μ, and premiums are received continuously at rate c = (1+θ)λμ. Which expression gives the infinite-time ruin probability ψ(u) for initial surplus u?

With exponential claims of mean μ and loading θ, ruin probability is ψ(u) = (1/(1+θ)) exp(−θu/((1+θ)μ)). The prefactor 1/(1+θ) is ψ(0), and the exponent uses the adjustment coefficient R = θ/((1+θ)μ).

  1. A(1/(1+θ)) exp(−θu/((1+θ)μ))Correct
  2. B(1/(1+θ)) exp(−θu/μ)
  3. C(1+θ) exp(−θu/((1+θ)μ))
  4. D(1/θ) exp(−θu/((1+θ)μ))
  5. exp(−θu/((1+θ)μ))

Explanation

For exponential claims the exact result is ψ(u) = (1/(1+θ)) exp(−θu/((1+θ)μ)). The adjustment coefficient is R = θ/((1+θ)μ), and ψ(0) = 1/(1+θ). Option 1 uses the wrong exponent, with μ instead of (1+θ)μ, so it understates the decay rate relationship.

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