Originally Posted by

**Rapid_W** Hi, I think I've done this right, however, i need to know if I have as there is no point me thinking I am right if I'm not, obviously.

**Dealer:**

U(x) = 2ln(x)

Initial Wealth = 500,000

Books = 10,000

Total Wealth = 510,000

Pr(complete loss of books) = 0.02

Pr(no loss) = 0.98

**Insurer:**

U(x) = ln(x + 200,000)

Assets = 2,000,000

**1** - The insurer initially offers the dealer a quote of £250. Find out if the dealer would accept this offer.

**2** - Find the maximum offer the dealer would accept.

**3** - The dealer offers to pay £201, find out if the insurer would accept this lower price.

**1)**

P:E[U(a-x)]=U(a-P)

E[U(a-x)] = (2ln(510000)*0.98)+(2ln(500000)*0.02)

E[U(a-x)] = 26.2835

26.2835 = 2ln(510000-P)

exp(13.14177) = 510000 - P

P = £201.948

As the initial offer is greater than P the initial offer would be rejected.

**2)**

The maximum quote the dealer would accept is £201.94 (rounding down as up would be more than the maximum)

**3)**

**Insurer without insuring**

U(x) = ln(2,000,000 + 200,000)

U(x) = ln(2,200,000)

U(x) = 14.60396792

**Insurer insuring**

U(x) = (ln(2,200,000 + 201) * 0.98) + (ln(2,200,000 + 201 - 10,000) * 0.02)

U(x) = 14.60396817

Utility function with insuring is greater than not insuring so the insurance company would accept the dealers quote of £201.

Does this method seem to be the right one? Are my conclusions correct?