On the stability of continuous-time portfolio problems with stochastic opportunity set

Mathematical Finance

Volumn 14, Issue 3, 2004, Pages 403-414

  Korn, Ralf ^a,b   Kraft, Holger ^b  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

Author keywords

Cox Ingersoll Ross model; Heston model; Optimal portfolios; Stochastic interest rate; Stochastic market price of risk; Stochastic volatility

Indexed keywords

EID: 3142710513     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0960-1627.2004.00197.x     Document Type: Article

References (22)

1. BAXTER, M. (1997): Generel Interest Rate-Models and the Universality of HJM; in Mathematics of Derivative Securities, M. A. H. Dempster and S. R. Pliska, eds. Cambridge: Cambridge University Press, 315-335.
2. BLACK, F., and P. KARASINSKI (1991): Bond and Option Pricing when the Short Rates are Lognormal, Financial Anal. J. 47, 52-59.
3. COX, J. C., and C. F. HUANG (1989): Optimal Consumption and Portfolio Policies when Asset Prices Follow a Diffusion Process, J. Econ. Theory 49, 33-83.
4. COX, J. C., and C. F. HUANG (1991): A Variational Problem Arising in Financial Economics, J. Math. Econ. 20, 465-487.
5. COX, J. C., J. E. INGERSOLL, JR., and S. A. Ross (1985): A Theory of the Term Structure of Interest Rates, Econometrica 53, 385-407.
6. DUFFIE, D. (1992): Dynamic Asset Pricing Theory, Princeton, NJ: Princeton University Press.
7. DYBVIG, P. H., L. C. G. ROGERS, and K. BACK (1999): Portfolio Turnpikes, Rev. Financial Stud. 12, 165-195.
8. FLEMING, W. H., and H. M. SONER (1993): Controlled Markov Processes and Viscosity Solutions. New York: Springer.
9. HESTON, S. L. (1993): A Closed Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Rev. Financial Stud. 6, 327-343.
10. KARATZAS, I., J. P. LEHOCZKY, and S. E. SHREVE (1987): Optimal Portfolio and Consumption Decisions for a Small Investor on a Finite Horizon, SIAM J. Control Optim. 27, 1157-1186.
11. KARATZAS, I., and S. E. SHREVE (1991): Brownian Motion and Stochastic Calculus. New York: Springer.
12. KARATZAS, I., and S. E. SHREVE (1998): Methods of Mathematical Finance. New York: Springer.
13. KORN, R. (1997): Optimal Portfolios. Singapore: World Scientific.
14. KORN, R., and H. KRAFT (2001): A Stochastic Control Approach to Portfolio Problems with Stochastic Interest Rates, SIAM J. Control Optim. 40, 1250-1269.
15. LIOUI, A., and P. PONCET (2001): On Optimal Portfolio Choice under Stochastic Interest Rates, J. Econ. Dynam. Control 25, 1841-1865.
16. Liu, J. (200la): Portfolio Selection in Stochastic Environments. Working paper, UCLA, Los Angeles.
17. Liu, J. (2001b): Dynamic Portfolio Choice and Risk Aversion. Working paper, UCLA, Los Angeles.
18. Liu, J., F. A. LONGSTAFF, and J. PAN (2003): Dynamic Asset Allocation with Event Risk, J. Finance 58, 231-259.
19. MERTON, R. C. (1969): Lifetime Portfolio Selection under Uncertainty: The Continuous Case, Rev. Econo. Stat. 51, 247-257.
20. MERTON, R. C. (1971): Optimal Consumption and Portfolio Rules in a Continuous-Time Model, J. Econ. Theory 3, 373-413. Erratum: ebenda 6 (1973), 213-214.
21. PLISKA, S. R. (1986): A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios, Math. Oper. Res. 11, 371-382.
22. SANDMANN, K., and D. SONDERMANN (1997): A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures, Math. Finance 7, 119-125.