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Dynamic Optimization of Long‐Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility
Author(s) -
Akian Marianne,
Sulem Agnès,
Taksar Michael I.
Publication year - 2001
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00111
Subject(s) - ergodic theory , variational inequality , bellman equation , mathematics , portfolio , stochastic control , transaction cost , limit (mathematics) , mathematical optimization , portfolio optimization , optimal control , economics , optimization problem , logarithm , mathematical economics , finance , mathematical analysis
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.