Answer to Question #192296 in Financial Math for Muhammad Umair

Question

What is meant by actuarially fair prices? What conditions will make Arrow-Debreu prices actuarially fair?

b) Using a model of incomplete market of your choice explain the consumption correlation puzzle.

Answer 1

(a)

Actuarially fair prices is an insurance policy, which is exactly equal to expected monetary losses. Actuarially fair insurance used to expect for the net paying off to the zero. An insurance contract is actuarially fair, when the payment of the premiums equals to an expected value for receiving the compensation from the customer's point of view.

Actuarially fair prices conditions:-

1) Actuarial fairness - Regarding ρ > 0, contingent used to claim that the prices will be actuarially fair that has [P(s)/P(S') = π(S)/π(S')]

[P(s)/P(S') = π(S)/π(S')], where an output of world will have the same states of the nature. 

a) Hence, requirement regarding an actuarial fairness for an absence of an uncertainty at the level of aggregate.

2) Non-actuarial fairness - When the world output has S' > output in S, an equation p(s) used to increase. Also, state S as the consumption that is premium, whereas the S' used to sell it in discount.

 

(b)

Incomplete market is a market in which Arrow-Debreu securities are less compared to the number of states. The shortage of securities restricts the flow of wealth between states. Incompleteness of the market is also due to lack of information between the agents. 

In an incomplete market, the consumption correlation puzzle suggests that consumption growth correlation is less in comparison to output growth correlation. This means that consumption and output does not move in the same direction when there is lack of complete information. 

Thus it can be concluded that, correlation between consumption and output is positively related in case of complete information, it is not positively related when there is constraints to flow of information.