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
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

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

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

Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$

Use LaTeX to type formulas and markdown to format text. See example.