An individual has $2000 in physical assets, and $600 in cash initially. This person faces the following loss distribution to the wealth. Full insurance is available at $600 Probability Loss
0.5 0
0.1 200
0.2 400
0.1 1000
0.1 2000

The Individual can also buy partial insurance with i. a $200 deductible, or ii. 75% coinsurance, or iii. Upper limit on coverage, with the limit being $1000. The premium on each partial coverage policy is $450.

Required:
Provide a ranking of the four types of policies for the individual, in terms of preference if the preference function is given by U(FW) = LN(1+FW), where FW is final wealth of the individual.

Answer with Explanation:

Probability   Expected Loss           Loss Forecast

0.5                          0                                0

0.1                        200                              20

0.2                       400                              80

0.1                       1000                             100

0.1                       2000                            200

1.00                     Total                             400

Now,

A. Final Wealth with no Insurance = Physical Assets of the person + Cash Assets - Total Loss Forecast

By putting values, we have:

Final Wealth with no Insurance = $2,000 + $600 - $400 = $2,200

B. For Full insurance, we will not consider expected loss because we will receive Insurance Premium instead:

Final Wealth with Full Insurance = Physical Assets + Cash Assets - Insurance Premium

By putting values, we have:

Final Wealth with Full Insurance = $2,000 + $600 - $600 = $2,000

C. Final Wealth with Partial Insurance and $200 deductibles = Physical Assets + Cash Assets - Insurance Premium For Partial Coverage - Deductible

By putting values, we have:

Final Wealth with Partial Insurance and $200 deductibles = $2,000 + $600 - $450  - $200 = $1,950

D. Final Wealth with 75% Co-insurance = Physical Assets + Cash Assets - Insurance Premium - Co-payment

By putting values, we have:

Final Wealth with 75% Co-Insurance = $2,000 + $600 - $450 - (75% * $400)

= $1,850

E. Final Wealth with Partial Insurance and $1,000 Upper Limit = Physical Assets + Cash Assets - Insurance Premium - Maximum Loss Expected

By putting values, we have:

= $2,000 + $600 - $450 - (Probability 0.1 * $2,000) = $1950

From the above, we can say that the best option here in descending order is as under:

1.  A. Final Wealth with no Insurance

2.  B. With Full insurance

3.  C. Final Wealth with Partial Insurance and $200 deductibles & E. Final Wealth with Partial Insurance and $1,000 Upper Limit

4.  E. Final Wealth with Partial Insurance and $1,000 Upper Limit