Mention the formula to be used to compute P ( A and B ) . Check whether the value is P ( A and B ) ≠ 0 . Explain it.

Question

We consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2

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Question

Chapter 4.2, Problem 12P

a.

To determine

Mention the formula to be used to compute P(A and B).

Check whether the value is P(A and B)≠0. Explain it.

b.

To determine

Explain whether the events A and B are not mutually exclusive.

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