IAI Actuarial Core Principles · Economic Modelling · Ruin theory
Which statement correctly distinguishes finite-time from ultimate ruin probability for a given surplus process?
Finite-time ruin probability is never larger than ultimate ruin probability. Ruin within a limited horizon is a subset of ruin at any time, so ψ(u,t) rises with t and converges to ψ(u).
- AFinite-time ruin probability ψ(u,t) is never larger than ultimate ruin probability ψ(u)Correct
- BFinite-time ruin probability ψ(u,t) can exceed ψ(u) for large t
- CUltimate ruin probability is always zero when u is positive
- DFinite-time ruin probability decreases as the time horizon t increases
- Ultimate ruin probability depends only on the claim frequency
Explanation
Ruin by time t is a subset of ruin at any time, so ψ(u,t) ≤ ψ(u) and ψ(u,t) is non-decreasing in t, tending to ψ(u). Ultimate ruin is not zero in general and depends on claim size distribution and loading too.
Did you get it right without looking?
One question tells you little. A timed set on Ruin theory shows your real accuracy, how long you take and where you lose marks.
More Ruin theory questions
- A compound Poisson surplus process has exponential claims with mean ₹50,000 and premium loading θ = 0.25. What is the probability of ultimat…
- In the classical compound Poisson surplus model, claims arrive at Poisson rate λ, individual claims are exponential with mean μ, and premium…
- For a compound Poisson surplus process with exponential claims of mean Rs 5 lakh and relative safety loading θ = 0.25, the ruin probability …
- In the compound Poisson model, Lundberg's inequality gives ψ(u) ≤ e^{-Ru}. If the insurer increases its premium loading while claim distribu…
- Under the Lundberg inequality psi(u) <= exp(-R u), an insurer with adjustment coefficient R=0.02 per Rs lakh holds initial surplus u=Rs 150 …
- An insurer has adjustment coefficient R = 0.02 per ₹ lakh. Using Lundberg's inequality, which initial surplus u (in ₹ lakh) guarantees that …