A note on the optimal portfolio problem in discrete processes

Naoyuki Ishimura; Yuji Mita

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 681-688
  • ISSN: 0023-5954

Abstract

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We deal with the optimal portfolio problem in discrete-time setting. Employing the discrete Itô formula, which is developed by Fujita, we establish the discrete Hamilton–Jacobi–Bellman (d-HJB) equation for the value function. Simple examples of the d-HJB equation are also discussed.

How to cite

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Ishimura, Naoyuki, and Mita, Yuji. "A note on the optimal portfolio problem in discrete processes." Kybernetika 45.4 (2009): 681-688. <http://eudml.org/doc/37718>.

@article{Ishimura2009,
abstract = {We deal with the optimal portfolio problem in discrete-time setting. Employing the discrete Itô formula, which is developed by Fujita, we establish the discrete Hamilton–Jacobi–Bellman (d-HJB) equation for the value function. Simple examples of the d-HJB equation are also discussed.},
author = {Ishimura, Naoyuki, Mita, Yuji},
journal = {Kybernetika},
keywords = {optimal portfolio problem; discrete Itô formula; discrete Hamilton–Jacobi–Bellman equation; optimal portfolio problem; discrete Ito formula; discrete Hamilton-Jacobi-Bellman equation},
language = {eng},
number = {4},
pages = {681-688},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A note on the optimal portfolio problem in discrete processes},
url = {http://eudml.org/doc/37718},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Ishimura, Naoyuki
AU - Mita, Yuji
TI - A note on the optimal portfolio problem in discrete processes
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 681
EP - 688
AB - We deal with the optimal portfolio problem in discrete-time setting. Employing the discrete Itô formula, which is developed by Fujita, we establish the discrete Hamilton–Jacobi–Bellman (d-HJB) equation for the value function. Simple examples of the d-HJB equation are also discussed.
LA - eng
KW - optimal portfolio problem; discrete Itô formula; discrete Hamilton–Jacobi–Bellman equation; optimal portfolio problem; discrete Ito formula; discrete Hamilton-Jacobi-Bellman equation
UR - http://eudml.org/doc/37718
ER -

References

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  1. Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem, Proc. Japan Acad., Ser. A. 84 (2008), 11–14. MR2381178
  2. Arbitrage Theory in Continuous Time, Second edition. Oxford Univ. Press, Oxford 2004. 
  3. Security Markets, Academic Press, London 1988. Zbl0861.90019MR0955269
  4. Introduction to the Stochastic Analysis for Financial Derivatives (Finance no Kakuritsu-Kaiseki Nyumon), Kodan-shya, Tokyo 2002 (in Japanese). 
  5. A proof of Itô’s formula using a discrete Itô’s formula, Stud. Scienti. Math. Hungarica 45 (2008), 125–134. MR2401170
  6. Option Pricing and Portfolio Optimization, Graduate Studies in Mathematics 31, American Mathematical Society, Rhode Island 2001. MR1802499
  7. Financial Markets, Translations of Mathematical Monographs 184, American Mathematical Society, Rhode Island 1999. Zbl1136.91013MR1687479
  8. Stochastic Processes for Insurance and Finance, John Wiley & Sons, New York 1998. MR1680267

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