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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

In the classical compound Poisson surplus process with initial surplus u, premium loading θ > 0 and exponentially distributed claim sizes with mean μ, which expression gives the probability of ultimate ruin ψ(u)?

The ruin probability is (1/(1+θ)) times exp(−θu/(μ(1+θ))). The initial ruin probability at zero surplus is 1/(1+θ), and the exponent uses the adjustment coefficient θ/(μ(1+θ)), which applies to exponential claims with mean μ.

  1. Aψ(u) = (1/(1+θ)) exp(−θu/(μ(1+θ)))Correct
  2. Bψ(u) = (1/(1+θ)) exp(−θu/μ)
  3. Cψ(u) = (1+θ) exp(−θu/(μ(1+θ)))
  4. Dψ(u) = exp(−θu/(μ(1+θ)))
  5. ψ(u) = (θ/(1+θ)) exp(−θu/(μ(1+θ)))

Explanation

For exponential claims with mean μ the ruin probability is ψ(u) = (1/(1+θ)) exp(−θu/(μ(1+θ))). The adjustment coefficient is R = θ/(μ(1+θ)) and ψ(0) = 1/(1+θ). Omitting the leading factor, as in the fourth option, would give ψ(0)=1, which is wrong for θ>0.

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