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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

In the compound Poisson model, Lundberg's inequality gives ψ(u) ≤ e^{-Ru}. If the insurer increases its premium loading while claim distribution is unchanged, what happens to R and to the Lundberg bound for a fixed initial surplus u > 0?

R increases and the bound becomes smaller. A higher premium rate raises the line λ + cr, moving the positive root to the right, and a larger R makes e^{-Ru} smaller for any positive initial surplus, so ruin is bounded as less likely.

  1. AR increases and the bound becomes smallerCorrect
  2. BR decreases and the bound becomes smaller
  3. CR increases and the bound becomes larger
  4. DR is unchanged because it depends only on claims
  5. R decreases and the bound becomes larger

Explanation

Higher c shifts the line λ + cr upward relative to λ M_X(r), so the positive root moves to the right and R rises. A larger R makes e^{-Ru} smaller for u > 0. R depends on premium rate as well as claims, so option 4 is wrong.

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