Consider a portfolio with one risky security and a risk free security. Suppose the price of the risky asset at time 0 is 4 and the possible values of the t = 1 price are 1.1, 2.2 and 3.3 (three possible states of the world at the end of a single trading period). Let the risk free interest rate r be 0.1 and take the price of the risk free security at t = 0 to be unity.

(a) Show that the trading strategy: h₀ = 4 and h₁ = −1 is a dominant trading strategy that starts with zero wealth and ends with positive wealth with certainty. 

(b) Find the discounted gain G^∗ over the single trading period. 

(c) Find a trading strategy that starts with negative wealth and ends with nonnegative wealth with certainty.