Optimal long-term investment model with memory

Applied Mathematics and Optimization

Volumn 55, Issue 1, 2007, Pages 93-122

  Inoue, Akihiko ^a   Nakano, Yumiharu ^b  

^a HOKKAIDO UNIVERSITY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

Large deviations; Long term investment; Optimal investment; Processes with memory; Processes with stationary increments; Riccati equations

Indexed keywords

GAUSSIAN PROCESSES; INFINITE HORIZONS; LARGE DEVIATIONS; STATIONARY INCREMENTS;

BROWNIAN MOVEMENT; MATHEMATICAL MODELS; OPTIMIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING; RICCATI EQUATIONS;

INVESTMENTS;

EID: 33846869954     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-006-0867-0     Document Type: Article

References (33)

1. V. Anh and A. Inoue. Financial markets with memory, I: Dynamic models. Stochastic Anal. Appl., 23:275-300, 2005.
2. V. Anh, A. Inoue, and Y. Kasahara. Financial markets with memory, II: Innovation processes and expected utility maximization. Stochastic Anal. Appl., 23:301-328, 2005.
3. V. Anh, A. Inoue, and C. Pesee. Incorporation of memory into the Black-Scholes-Merton theory and estimation of volatility. Preprint.
4. O. E. Barndorff-Nielsen, E. Nicalato, and N. Shephard. Some recent developments in stochastic volatility modelling. Quant. Finance, 2:11-23, 2002.
5. O. E. Barndorff-Nielsen and N. Shephard. Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. J. Roy. Statist. Soc. Ser. B, 63:167-241, 2001.
6. T. R. Bielecki and S. R. Pliska. Risk sensitive dynamic asset management. Appl. Math. Optim., 39:337-360, 1999.
7. F. Comte and E. Renault. Long memory continuous-time models. J. Econometrics, 73:101-149, 1996.
8. F. Comte and E. Renault. Long memory in continuous-time stochastic volatility models. Math. Finance, 8:291-323, 1998.
9. R. J. Elliott and J. van der Hoek. A general fractional white noise theory and applications to finance. Math. Finance, 13:301-330, 2003.
10. W. H. Fleming and R. W. Rishel. Deterministic and Stochastic Optimal Control. Springer-Verlag, New York, 1975.
11. W. H. Fleming and S. J. Sheu. Risk-sensitive control and an optimal investment model. Math. Finance, 10:197-213, 2000.
12. W. H. Fleming and S. J. Sheu. Risk-sensitive control and an optimal investment model (II). Ann. Appl. Probab., 12:730-767, 2000.
13. H. Hata and Y. Iida. A risk-sensitive stochastic control approach to an optimal investment problem with partial information. Finance Stoch., 10:395-426, 2006.
14. H. Hata and J. Sekine. Solving long term optimal investment problems with Cox-Ingersoll-Ross interest rates. Adv. Math. Econ., 8:231-255, 2006.
15. H. Hata and J. Sekine. Solving a large deviations control problem with a nonlinear factor model. Preprint.
16. C. C. Heyde. A risky asset model with strong dependence through fractal activity time. J. Appl. Probab., 36:1234-1239, 1999.
17. C. C. Heyde and N. N. Leonenko. Student processes. Adv. in Appl. Probab., 37:342-365, 2005.
18. Y. Hu and B. Øksendal. Fractional white noise calculus and applications to finance. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6:1-32, 2003.
19. Y. Hu, B. Øksendal, and A. Sulem. Optimal consumption and portfolio in a Black-Scholes market driven by fractional Brownian motion. Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6:519-536, 2003.
20. A. Inoue, Y. Nakano, and V. Anh. Linear filtering of systems with memory and application to finance. J. Appl. Math. Stochastic Anal., Art. ID 53104, 26 pp., 2006.
21. I. Karatzas and S. E. Shreve. Methods of Mathematical Finance. Springer-Verlag, New York, 1998.
22. K. Kuroda and H. Nagai. Risk sensitive portfolio optimization on infinite time horizon. Stoch. Stoch. Rep., 73:309-331, 2002.
23. R. S. Liptser and A. N. Shiryayev. Statistics of Random Processes. I. General Theory, 2nd edn. Springer-Verlag, New York, 2001.
24. D. G. Luenberger, Investment Science, Oxford University Press, Oxford, 1998.
25. R. Merton. Optimal consumption and portfolio rules in a continuous time model. J. Econom. Theory, 3:373-413, 1971.
26. L. E. Myers. Survival functions induced by stochastic covariance processes. J. Appl. Probab., 18:523-529, 1981.
27. H. Nagai and S. Peng. Risk-sensitive dynamic portfolio optimization with partial information on infinite time horizon. Ann. Appl. Probab., 12:173-195, 2002.
28. H. Pham. A large deviations approach to optimal long term investment. Finance Stoch., 7:169-195, 2003.
29. H. Pham. A risk-sensitive control dual approach to a large deviations control problem. Systems Control Lett., 49:295-309, 2003.
30. L. C. G. Rogers. Arbitrage with fractional Brownian motion. Math. Finance, 7:95-105, 1997.
31. L. C. G. Rogers and D. Williams. Diffusions, Markov Processes and Martingales, Vol. 2, 2nd edn. Cambridge University Press, Cambridge, 2000.
32. W. Willinger, M. S. Taqqu, and V. Teverovsky. Stock market prices and long-range dependence. Finance Stoch., 3:1-13, 1999.
33. Yahoo! Inc. Yahoo! Finance, http://finance.yahoo.com/.