A note on the optimal portfolio problem in discrete processes
Kybernetika, Tome 45 (2009) no. 4, pp. 681-688 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 49L20, 90C90, 91B28, 91B30, 91G10
Keywords: optimal portfolio problem; discrete Itô formula; discrete Hamilton–Jacobi–Bellman equation
@article{KYB_2009_45_4_a11,
     author = {Ishimura, Naoyuki and Mita, Yuji},
     title = {A note on the optimal portfolio problem in discrete processes},
     journal = {Kybernetika},
     pages = {681--688},
     year = {2009},
     volume = {45},
     number = {4},
     mrnumber = {2588633},
     zbl = {1190.49034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_4_a11/}
}
TY  - JOUR
AU  - Ishimura, Naoyuki
AU  - Mita, Yuji
TI  - A note on the optimal portfolio problem in discrete processes
JO  - Kybernetika
PY  - 2009
SP  - 681
EP  - 688
VL  - 45
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2009_45_4_a11/
LA  - en
ID  - KYB_2009_45_4_a11
ER  - 
%0 Journal Article
%A Ishimura, Naoyuki
%A Mita, Yuji
%T A note on the optimal portfolio problem in discrete processes
%J Kybernetika
%D 2009
%P 681-688
%V 45
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2009_45_4_a11/
%G en
%F KYB_2009_45_4_a11
Ishimura, Naoyuki; Mita, Yuji. A note on the optimal portfolio problem in discrete processes. Kybernetika, Tome 45 (2009) no. 4, pp. 681-688. http://geodesic.mathdoc.fr/item/KYB_2009_45_4_a11/

[1] R. Abe and N. Ishimura: Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem. Proc. Japan Acad., Ser. A. 84 (2008), 11–14. | MR

[2] T. Björk: Arbitrage Theory in Continuous Time. Second edition. Oxford Univ. Press, Oxford 2004.

[3] D. Duffie: Security Markets. Academic Press, London 1988. | MR | Zbl

[4] T. Fujita: Introduction to the Stochastic Analysis for Financial Derivatives (Finance no Kakuritsu-Kaiseki Nyumon). Kodan-shya, Tokyo 2002 (in Japanese).

[5] T. Fujita and Y. Kawanishi: A proof of Itô’s formula using a discrete Itô’s formula. Stud. Scienti. Math. Hungarica 45 (2008), 125–134. | MR

[6] R. Korn and E. Korn: Option Pricing and Portfolio Optimization. Graduate Studies in Mathematics 31, American Mathematical Society, Rhode Island 2001. | MR

[7] A. V. Melnikov: Financial Markets. Translations of Mathematical Monographs 184, American Mathematical Society, Rhode Island 1999. | MR | Zbl

[8] T. Rolski, H. Schmidli, V. Schmidt, and J. Teugels: Stochastic Processes for Insurance and Finance. John Wiley & Sons, New York 1998. | MR