There are two assets A and B in a two-state economy. Their current prices, possible payoffs and associated probabilities are shown in the following table. The risk-free interest rate over the next period is unknown.

	A	B	Physical probability
Current price	22	11
Payoff in state 1	30	15	0.6
Payoff in state 2	15	8	0.4

1. Is this market complete? Explain.

2. Calculate the risk-neutral probabilities, state prices, the stochastic discount factors (SDF) for the two states, and the risk-free interest rate over the next period.

3. Is there any arbitrage opportunity? Design a trading strategy to exploit the arbitrage opportunity. Assume that all assets are infinitely divisible and short sales are allowed.

4. Explain why risk neutral probabilities are important in asset pricing.