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Dynamic optimization of long-term growth rate for a portfolio with transaction costs and logarithmic utility. (English) Zbl 1055.91016

Summary: We study the optimal investment policy for an investor who has available one bank account and \(n\) risky assets modeled by log-normal diffusions. The objective is to maximize the long-run average growth of wealth for a logarithmic utility function in the presence of proportional transaction costs. This problem is formulated as an ergodic singular stochastic control problem and interpreted as the limit of a discounted control problem for vanishing discount factor. The variational inequalities for the discounted control problem and the limiting ergodic problem are established in the viscosity sense. The ergodic variational inequality is solved by using a numerical algorithm based on policy iterations and multigrid methods. A numerical example is displayed for two risky assets.

MSC:

91B28 Finance etc. (MSC2000)
49N90 Applications of optimal control and differential games
93E20 Optimal stochastic control
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