Dynamic Optimization of Long-Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility |
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Authors: | Marianne Akian Agnès Sulem & Michael I Taksar |
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Institution: | INRIA, Domaine de Voluceau, Le Chesnay Cedex, France,;Department of Applied Mathematics and Statistics, SUNY at Stony Brook |
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Abstract: | 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. |
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Keywords: | singular ergodic stochastic control viscosity solution variational inequality portfolio selection transaction costs |
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