The solid line shows the log optimal investment

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Unformatted text preview: Σ is diagonal. 13.5 Log-optimal investment strategy. In this problem you will solve a specific instance of the log-optimal investment problem described in exercise 4.60, with n = 5 assets and m = 10 possible outcomes in each period. The problem data are defined in log_opt_invest.m, with the rows of the matrix P giving the asset return vectors pT . The outcomes are equiprobable, i.e., we have πj = 1/m. Each j column of the matrix P gives the return of the associated asset in the different posible outcomes. You can examine the columns to get an idea of the types of assets. For example, the last asset gives a fixed and certain return of 1%; the first asset is a very risky one, with occasional large return, and (more often) substantial loss. ⋆ Find the log-optimal investment strategy x⋆ , and its associated long term growth rate Rlt . Compare this to the long term growth rate obtained with a uniform allocation strategy, i.e., x = (1/n)1, and also with a pure investment in each asset. For the o...
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