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Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I by Eric Chin, Sverrir Olafsson, Dian Nel

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4.2.3 Risk-Neutral Measure

  1. 1. Geometric Brownian Motion. Consider an economy consisting of a risk-free asset and a stock price (risky asset). At time c04-math-819, the risk-free asset c04-math-820 and the stock price c04-math-821 have the following diffusion processes
    equation

    where c04-math-822 is the risk-free rate, c04-math-823 is the stock price drift rate, c04-math-824 is the stock price volatility(which are all time dependent) and c04-math-825 is a c04-math-826-standard Wiener process on the probability space c04-math-827.

    From the following discounted stock price process

    show, using Girsanov's theorem, ...

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