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Reweighting a rare loss

Expected valueEasy

A trade loses $3000$ with true probability $0.5%$ a day and loses nothing otherwise. A simulator draws the loss day with probability $10%$ instead. In $200$ draws, $24$ are loss days. What is the importance sampling estimate of the expected daily loss? Answer with a number.

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Hint

A loss day carries the weight true probability over sampling probability.

Solution

The weight of a loss day is $0.5%/10% = \frac{1}{20}$ .
Each loss day scores $3000 \times \frac{1}{20} = 150$ .
The estimate is $24 \times \frac{150}{200} = 18$ , so the answer is $18$ .

Answer: $18$

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