East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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OPTIMAL PORTFOLIO CHOICE IN A BINOMIAL-TREE AND ITS CONVERGENCE

  • Jeong, Seungwon (Department of Financial Engineering, School of Business, Ajou University) ;
  • Ahn, Sang Jin (Department of Financial Engineering, School of Business, Ajou University) ;
  • Koo, Hyeng Keun (Department of Financial Engineering, School of Business, Ajou University) ;
  • Ahn, Seryoong (Division of Business Administration, Pukyong National University)
  • Received : 2022.01.03
  • Accepted : 2022.03.08
  • Published : 2022.05.18
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Abstract

This study investigates the convergence of the optimal consumption 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 policies 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.

Keywords

Acknowledgement

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea(NRF-2021S1A5A2A03063960).

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