2. We derived a geometric BM model for ones\'s total wealth evolution, where the

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2. We derived a geometric BM model for ones's total wealth evolution, where the alpha's, mu's and sigma's were given, as well as the correlations of the component BM processes within a n-dim BM {B,/ z0}. Suppose that a geometric BM model is also given for the riskless rate (r): the arithmetic mean is delta and the volatility is tau; let the BM for the rate be denoted by {C,10 Suppose that the correlations of its BM with the BM's for each of your n securities are also given. Derive a probability of regret formula for this setting, extending what we derived in class So Wo e'T in the formula is replaced by: This is not a good model for r, but it was one of the first used [Rendleman and Bartter (1980), The pricing of options on debt securities, Journal of Financial and Quantitative Analysis, Vol 15, March, 11-24. Why, based on your intuition, is it not a good model for r (just one sentence is enough)?

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