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Numerical Schemes for Investment Models with Singular Transactions.



This paper considers an infinite horizon investment-consumption model in which a single agent consumes and distributes his wealth between two assets, a bond and a stock. The problem of maximization of the total utility from consumption is treated, when state (amount allocated in assets) and control (consumption, rates of trading) constraints are present. The value function is characterized as the unique viscosity solution of the Hamilton-Jacobi-Bellman equation which, actually, is a Variational Inequality with gradient constraints. Numerical schemes are then constructed in order to compute the value function and the location of the free boundaries of the so-called transaction regions. These schemes are a combination of implicit and explicit schemes; their convergence is obtained from the uniqueness of viscosity solutions to the HJB equation. Citation Copyright 1994 by Kluwer Academic Publishers.

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