IAI Actuarial Core Principles · Economic Modelling · Ruin theory
In a compound Poisson surplus process, claims are exponential with mean 1,000 rupees and arrive at rate λ = 5 per year. Premiums are received at rate c = 10,000 rupees per year. What is the adjustment coefficient R (per rupee)?
R = 1/μ − λ/c = 0.001 − 0.0005 = 0.0005 per rupee. This satisfies λ + cr = λ/(1 − μr), since both sides equal 10.
- A0.0004
- B0.0005Correct
- C0.0006
- D0.0008
- 0.0010
Explanation
For exponential claims R = 1/μ − λ/c = 0.001 − 5/10,000 = 0.001 − 0.0005 = 0.0005. Check: λ+cr = 5+5 = 10; λ/(1−μr)=5/(0.5)=10. A distractor of 0.0008 would come from not dividing correctly.
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
- For a classical surplus process, which statement about the Lundberg inequality ψ(u) ≤ e^{−Ru} is correct?
- A simulation of annual surplus uses U_n = U_{n-1} + 5 − X_n (Rs crore), with X_n lognormal i.i.d. Which change would most clearly reduce the…
- 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…
- 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 …
- For a compound Poisson surplus process with exponential claims of mean Rs 5 lakh and relative safety loading θ = 0.25, the ruin probability …