IAI Actuarial Core Principles · Economic Modelling · Ruin theory
Claims are exponential with mean Rs 5 lakh, and θ = 0.25. Using ψ(u) = (1/(1+θ)) exp(−θu/((1+θ)μ)), what is the adjustment coefficient R, and which is the correct value of ψ(u) when u = Rs 25 lakh expressed as 0.8·e^(−x)?
R is 0.04 per lakh and ψ(25) = 0.8e^(−1). R = θ/((1+θ)μ) = 0.25/(1.25×5) = 0.04, and multiplying by u = 25 gives an exponent of 1.0.
- AR = 0.04 per lakh, x = 0.5
- BR = 0.04 per lakh, x = 1.0Correct
- CR = 0.05 per lakh, x = 1.25
- DR = 0.05 per lakh, x = 0.8
- R = 0.25 per lakh, x = 6.25
Explanation
R = θ/((1+θ)μ) = 0.25/(1.25×5) = 0.04 per lakh. Then x = Ru = 0.04 × 25 = 1.0, so ψ = 0.8e^(−1). Using R = θ/μ = 0.05 ignores the (1+θ) factor and is wrong.
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
- 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 …
- Which statement correctly distinguishes finite-time from ultimate ruin probability for a given surplus process?
- An insurer has adjustment coefficient R = 0.02 per ₹ lakh. Using Lundberg's inequality, which initial surplus u (in ₹ lakh) guarantees that …