Portfolio Optimization With Markov-Modulated Stock Prices and Interest Rates

IEEE Transactions on Automatic Control

Volumn 49, Issue 3, 2004, Pages 442-447

  Bäuerle, Nicole ^a   Rieder, Ulrich ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

Markov modulation; Stochastic control; Utility maximization; Verification theorem

Indexed keywords

FINANCE; MARKOV PROCESSES; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS;

MARKOV MODULATION; UTILITY MAXIMIZATION; VERIFICATION THEOREM;

STOCHASTIC CONTROL SYSTEMS;

EID: 11144355137     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.824471     Document Type: Article

References (23)

1. S. Browne, "Reaching goals by deadline: Digital options and continuous-time active portfolio management," Adv. Appl. Probab., vol. 31, pp. 551-577, 1999.
2. M. H. A. Davis, Markov Models and Optimization, London, U.K.: Chapman and Hall, 1993.
3. G. B. Di Masi, Y. M. Kabanov, and W. J. Runggaldier, "Mean-variance hedging of options on stocks with Markov volatilities," Theory Probab. Appl., vol. 39, pp. 211-222, 1994.
4. W. H. Fleming and D. Herńndez-Herńndez, "An optimal consumption model with stochastic volatility," Finance Stoch., vol. 7, pp. 245-262, 2003.
5. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control. New York: Springer-Verlag, 1975.
6. W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions. New York: Springer-Verlag, 1993.
7. H. Föllmer and P. Leukert, "Quantile hedging," Finance Stoch., vol. 3, pp. 251-273, 1999.
8. J. P. Fouque, G. Papanicolaou, and K. R. Sircar, Derivatives in Financial Markest with Stochastic Volatility. Cambridge, U.K.: Cambridge Univ. Press, 2000.
9. R. Frey and W. J. Runggaldier, "A nonlinear filtering approach to volatility estimation with a view toward high frequency data," Int. J. Theoret. Appl. Finance, vol. 4, pp. 199-210, 2001.
10. T. Goll and J. Kallsen, "Optimal portfolios for logarithmic utility," in Stoch. Proc. Appl., vol. 89, 2000, pp. 31-48.
11. S. Heston, "A closed-form solution for options with stochastic volatility with applications to bond and currency options," Rev. Financial Stud., vol. 6, pp. 327-343, 1993.
12. T. S. Y. Ho and S. B. Lee, "Term structure movements and pricing interest contingent claims," J. Finance, vol. 41, pp. 1011-1029, 1986.
13. J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes. New York: Springer-Verlag, 1987.
14. R. Korn and H. Kraft, "A stochastic control approach to portfolio problems with stochastic interest rates," SIAM J. Control Optim., vol. 40, pp. 1250-1269, 2001.
15. M. Kulldorff, "Optimal control of favorable games with a time limit," SIAM J. Control Optim., vol. 31, pp. 52-69, 1993.
16. H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time. New York: Springer-Verlag, 1992.
17. A. Lioui and P. Poncet, "On optimal portfolio choice under stochastic interest rates," J. Econ. Dyna. Control, vol. 25, pp. 1841-1865, 2001.
18. R. C. Merton, "Optimum consumption and portfolio rules in a continuous-time model," J. Econ. Theo., pp. 373-413, 1971.
19. H. Pham and M. C. Quenez, "Optimal portfolio in partially observed stochastic volatility models," Ann. Appl. Probab., vol. 11, pp. 210-238, 2001.
20. O. Vasicek, "An equilibrium characterization of the term structure," J. Financial Econ., vol. 5, pp. 177-188, 1977.
21. T. Zariphopoulou, "Optimal investment and consumption models with nonlinear stock dynamics," Math. Meth. Oper. Res., vol. 50, pp. 271-296, 1999.
22. _, "A solution approach to valuation with unhedgeable risks," Finance Stoch., vol. 5, pp. 61-82, 2001.
23. Q. Zhang, "Stock trading: An optimal selling rule," SIAM J. Control Optim., vol. 40, pp. 64-87, 2001.