In the per-loss formula, the term E[X ∧ m/(1+r)] caps X at what amount?

Study for the SOA Fundamentals of Actuarial Mathematics (FAM) Exam. Prepare with flashcards and multiple choice questions with detailed explanations. Get ready for your future as an actuary!

Multiple Choice

In the per-loss formula, the term E[X ∧ m/(1+r)] caps X at what amount?

Explanation:
The main idea is that the expression X ∧ m/(1+r) applies a cap to X by taking the smaller of the actual loss and the present-value limit. In this per-loss formula, the cap is the present value of the per-loss limit, m/(1+r). That means if a loss exceeds the limit, it is truncated down to m/(1+r) when calculating the expected value. The reason we use m/(1+r) is to reflect the time value of money; the policy limit m, when viewed in present value terms, equals m/(1+r). So the cap on X is exactly m/(1+r).

The main idea is that the expression X ∧ m/(1+r) applies a cap to X by taking the smaller of the actual loss and the present-value limit. In this per-loss formula, the cap is the present value of the per-loss limit, m/(1+r). That means if a loss exceeds the limit, it is truncated down to m/(1+r) when calculating the expected value. The reason we use m/(1+r) is to reflect the time value of money; the policy limit m, when viewed in present value terms, equals m/(1+r). So the cap on X is exactly m/(1+r).

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