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Consider stock price process (Geometric Brownian Motion): $$S_t=S_0exp((\mu-0.5\sigma^2)t+\sigma W_t) \tag{1}$$ where $W_t$ is a Wiener process and $\mu$ is a drift - or average return. If you are not familiar with Wiener process you can see this equation as: $$S_t=S_0exp((\mu-0.5\sigma^2)t+\sigma \sqrt t Z) \tag{2}$$ where $Z$ is standard normal random ...

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The answer is that $S_t$ is a random variable which has realizations that can be solved for using a monte carlo or numerical methods. By solving for this value many times (which is what a monte carlo does for instance) you can find a distribution of prices of the underlying at a given time. This is because the process is random so each solve should be ...

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Thank you Dimitri, that is indeed who I was thinking of! Kudos for closing this search off so quickly.

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The number of up moves of the stock $S$ after 100 days follows binomial distribution. To calculate expected value of the stock we have to weight values by probability mass function. After 100 days we have $k$ up moves of $1+10\%$ and $100-k$ down moves of $1-10\%$ i.e. the value of the stock is $S_0*(1+10\%)^k*(1-10\%)^{(100-k)}$ with probability \${100}\...

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