This preview shows page 1. Sign up to view the full content.
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
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,
πj T = 1,
xi > 0 ⇒
j =1 m xi = 0 ⇒ πj
j =1 pij
j We can interpret this as follows. pij /pT x is a random variable, which gives the ratio of the
investment gain with asset i only, to t...
View Full Document
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
- The Aeneid