Question: Consider the binomial asset pricing model. Assume the stocks current price is S 0 , the up factor is u, the down factor is d,

Consider the binomial asset pricing model. Assume the stocks current price is S₀, the up factor is u, the down factor is d, the risk-free interest rate is r and assume the no arbitrage condition holds. Let P(H) = p > 0. If Xn = S ² _n + S₀, for n 0, prove or disprove Xn is a martingale under the P probability measure if the expected return on the stock is positive.

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