An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year.

# An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year.

H
Asked by 2 years ago
240 points

An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year. If the company estimates that E will occur within a year with probability p, what should it charge the customer in order that its expected profit will be 10 percent of A?

An insurance
hansel

### 1 Answer

Answered by 2 years ago
8.7k points

The insurance company wants to make profit 0.1A, let C be the amount that the company changes a customer. The expected profit of the company is

$$C+p(-A)+(1-p)(0)=C-pA$$

and we need

$$C-pA=0.1A \longrightarrow C=\bigg(p+\frac{1}{10}\bigg)A$$

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Asked: 2 years ago