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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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  1. 9. Pricing a Security Derivative. Consider an economy consisting of a risk-free asset and a stock price (risky asset). At time c04-math-1094, the risk-free asset c04-math-1095 and the stock price c04-math-1096 have the following diffusion processes
    equation

    where c04-math-1097 is the risk-free rate, c04-math-1098 is the continuous dividend yield, c04-math-1099 is the stock price growth rate, c04-math-1100 is the stock price volatility (which are all time dependent) and c04-math-1101 is a c04-math-1102-standard Wiener process on the probability space .

    At time , we consider a trader who has a portfolio valued at holding ...

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