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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 logoptimal investment problem.
(a) Show that the optimality conditions for the logoptimal 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.
 Fall '13
 F.Borrelli
 The Aeneid

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