## PsUW0

This formula will be useful in our later work.

(c) If there are n states and at least n independent securities with known prices, and no arbitrage possibility, then the risk-neutral probabilities can be found directly by solving the system of equations s

Example 9.10 (The film venture) We found the state prices of the full film venture (with three securities) to be

= g, V'2 = 5, ^3 = 5 Multiplying these by the risk-free rate 1.2, we obtain the risk-neutral probabilities

9 J = 2> <72 = -6, 03 = 2. Hence the price of a security with payoff (c/1, c/2, d3) is

Here again, this pricing formula is valid only for the original securities or linear combinations of those securities. The risk-neutral probabilities were derived explicitly to price the original securities.

The risk-neutral pricing result can be extended to the general situation that does not assume that there are a finite number of states (See Exercise 15 )

## Retirement Planning For The Golden Years

If mutual funds seem boring to you, there are other higher risk investment opportunities in the form of stocks. I seriously recommend studying the market carefully and completely before making the leap into stock trading but this can be quite the short-term quick profit rush that you are looking for if you am willing to risk your retirement investment for the sake of increasing your net worth. If you do choose to invest in the stock market please take the time to learn the proper procedures, the risks, and the process before diving in. If you have a financial planner and you definitely should then he or she may prove to be an exceptional resource when it comes to the practice of 'playing' the stock market.

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