Question

The claim cost of an insurance company follows a normal distribution with an expected value of $500 million and a standard deviation of $100 million. Based on the above, work on the following questions.

1. In the graph, indicate the probability of insolvency of the insurer when it has an asset of $750 million. Please clearly label the axes.

2. Show the probability of insolvency of the insurer after the insurer raises $100 million of new capital.

3. Compute the probabilities of insolvency for the insurer when its total assets are respectively $750 and $850 million.

4. What is the firm’s value at risk at the 1% level?

   
   

Answer 1

(a)

x	750
µ	500
σ	100
z = (x - µ)/σ	2.5
p-value	0.9938

(b)

x	600
µ	500
σ	100
z = (x - µ)/σ	1
p-value	0.8413

(c)

x	750		x	850
µ	500		µ	500
σ	100		σ	100
z = (x - µ)/σ	2.5		z = (x - µ)/σ	3.5
p-value	0.9938		p-value	0.9998

(d)

z	-2.326348
x	267.3652