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Reports (Research Report) Year : 1999

Dynamic Optimisation of a Long Term Growth Rate for a Mixed Portfolio with Transaction Costs. The Logarithmic Utility Case

Abstract

This paper studies the optimal investment policy for an investor who has available one bank account with fixed interest rate and n risky assets whose prices are log-normal diffusions. Transactions between the assets incur proportional transaction costs. The objective is to maximize the long run average growth of wealth for a logarithmic utility function. This problem is formulated as a singular stochastic control problem with ergodic criterion and interpreted as the limit of a discounted control problem when the discount factor goes to zero. The dynamic programming variational inequalities for the discounted control problem and the the limiting ergodic problem are established in the viscosity sense. The "potentia- l function'' for the ergodic problem can be obtained as a limit of the value function of the discounted problem when the discount factor goes to zero. The ergodic variational inequality is solved by using a numerical algorithm based on policies iterations and multigrid methods. A numerical example is displayed for 2 risky assets.
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Dates and versions

inria-00073050 , version 1 (24-05-2006)

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  • HAL Id : inria-00073050 , version 1

Cite

Marianne Akian, Agnès Sulem, Michael I. Taksar. Dynamic Optimisation of a Long Term Growth Rate for a Mixed Portfolio with Transaction Costs. The Logarithmic Utility Case. [Research Report] RR-3626, INRIA. 1999. ⟨inria-00073050⟩
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