Question: Consider the stochastic processes that we have studied in our lectures. a) Illustrate in detail the fundamental properties of a generalized Wiener process. [7 marks]

Consider the stochastic processes that we have studied in our lectures.

a) Illustrate in detail the fundamental properties of a "generalized Wiener process".

[7 marks]

b) Discuss the so-called "lognormal property" of stock prices.

[10 marks]

c) Consider a stock price S=S(t), a function G=G(S, t) of the stock price S and time t, and suppose that the stock price follows a geometric Brownian motion process. Provide the mathematical formulation and the financial interpretation of It's lemma for the stochastic process followed by G=G(S, t).

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