Chapter 20, Problem 2P

To determine

To determine: What AIG assumed about the probabilities of defaults by different home-owners in the U.S market and if they were wrong and right.

Concept introduction

Expected Value: It is defined as the weighted average of probable events where the weights of each probable value corresponds to the chances of that value occurring. The formula to calculate the expected value is:

Where,

• is expected value.
  
• is probability of event 1.
  
• is probability of event 2.
  
• is probability of event N.
  
• is event 1.
  
• is event 2.
  
• is event N.
  

Expected Utility: It is defined as the value of a person’s total utility, so that there is no certainty for future results.

Marginal Utility: When there is an increase in total utility, then the amount of increase that happens due to variation in one unit is known as marginal utility. The formula to calculate marginal utility is:

or

Where,

• is marginal utility.
  
• is total utility.
  
• X is any quantity of goods.
• is the number of goods.
  

Risk Averse: When a person does not like risk then he is referred to as risk averse. In case of risk averse, the marginal utility is diminishing in nature which means that for every additional unit of good, marginal utility declines.