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Suppose that the stock market follows the dynamics dS_t = mu S_t dt + sigma S_t dW_t and the interest rate is constant and equal

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Suppose that the stock market follows the dynamics dS_t = mu S_t dt + sigma S_t dW_t and the interest rate is constant and equal to r. Consider a "digital claim"Phi (S_T) = {1 if S_T > K 0 if S_T 0. Give a formula for the arbitrage-free price II (S_t, t) of the digital claim at time t when the stock price is S_t

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