| Title:
|
A note on the optimal portfolio problem in discrete processes (English) |
| Author:
|
Ishimura, Naoyuki |
| Author:
|
Mita, Yuji |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
681-688 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
optimal portfolio problem |
| Keyword:
|
discrete Itô formula |
| Keyword:
|
discrete Hamilton–Jacobi–Bellman equation |
| MSC:
|
49L20 |
| MSC:
|
90C90 |
| MSC:
|
91B28 |
| MSC:
|
91B30 |
| MSC:
|
91G10 |
| idZBL:
|
Zbl 1190.49034 |
| idMR:
|
MR2588633 |
| . |
| Date available:
|
2010-06-02T19:05:41Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140060 |
| . |
| Reference:
|
[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 2381178 |
| Reference:
|
[2] T. Björk: Arbitrage Theory in Continuous Time.Second edition. Oxford Univ. Press, Oxford 2004. |
| Reference:
|
[3] D. Duffie: Security Markets.Academic Press, London 1988. Zbl 0861.90019, MR 0955269 |
| Reference:
|
[4] T. Fujita: Introduction to the Stochastic Analysis for Financial Derivatives (Finance no Kakuritsu-Kaiseki Nyumon).Kodan-shya, Tokyo 2002 (in Japanese). |
| Reference:
|
[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 2401170 |
| Reference:
|
[6] R. Korn and E. Korn: Option Pricing and Portfolio Optimization.Graduate Studies in Mathematics 31, American Mathematical Society, Rhode Island 2001. MR 1802499 |
| Reference:
|
[7] A. V. Melnikov: Financial Markets.Translations of Mathematical Monographs 184, American Mathematical Society, Rhode Island 1999. Zbl 1136.91013, MR 1687479 |
| Reference:
|
[8] T. Rolski, H. Schmidli, V. Schmidt, and J. Teugels: Stochastic Processes for Insurance and Finance.John Wiley & Sons, New York 1998. MR 1680267 |
| . |
