bv_cvxbook_extra_exercises

# The house determines x after examining all the

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Unformatted text preview: ptimal investment strategy, and also the uniform investment strategy, plot 10 sample trajectories of the accumulated wealth, i.e., W (T ) = W (0) T=1 λ(t), for T = 0, . . . , 200, with t initial wealth W (0) = 1. 105 To save you the trouble of ﬁguring out how to simulate the wealth trajectories or plot them nicely, we’ve included the simulation and plotting code in log_opt_invest.m; you just have to add the code needed to ﬁnd x⋆ . Hint: The current version of CVX handles the logarithm via an iterative method, which can be slow and unreliable. You’re better oﬀ using geo_mean(), which is directly handled by CVX, to solve the problem. 13.6 Optimality conditions and dual for log-optimal investment problem. (a) Show that the optimality conditions for the log-optimal investment problem described in exercise 4.60 can be expressed as: 1T x = 1, x 0, and for each i, m pij πj T = 1, xi > 0 ⇒ pj x j =1 m xi = 0 ⇒ πj j =1 pij ≤ 1. pT x j We can interpret this as follows. pij /pT x is a random variable, which gives the ratio of the j investment gain with asset i only, to t...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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