OPTIMAL PORTFOLIO CHOICE IN A BINOMIAL-TREE AND ITS CONVERGENCE
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This study investigates the convergence of the optimal con- sumption and investment policies in a binomial-tree model to those in the continuous-time model of Merton (1969). We provide the convergence in explicit form and show that the convergence rate is of order ∆t, which is the length of time between consecutive time points. We also show by numerical solutions with realistic parameter values that the optimal poli- cies in the binomial-tree model do not differ significantly from those in the continuous-time model for long-term portfolio management with a horizon over 30 years if rebalancing is done every 6 months.
Abstract
This study investigates the convergence of the optimal con- sumption and investment policies in a binomial-tree model to those in the continuous-time model of Merton (1969). We provide the convergence in explicit form and show that the convergence rate is of order ∆t, which is the length of time between consecutive time points. We also show by numerical solutions with realistic parameter values that the optimal poli- cies in the binomial-tree model do not differ significantly from those in the continuous-time model for long-term portfolio management with a horizon over 30 years if rebalancing is done every 6 months.
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