Convergence of discretized stochastic (interest rate) processes with stochastic drift term

Applied Stochastic Models and Data Analysis

Volumn 14, Issue 1, 1998, Pages 77-84

  Deelstra, G ^a   Delbaen, F ^b  

^a FREE UNIVERSITY OF BRUSSELS   (Belgium)

^b ETH ZURICH   (Switzerland)

Author keywords

Euler discretization scheme; H lder condition; Stochastic differential equation; Stochastic drift term; Strong convergence

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; CORRELATION METHODS; DIFFERENTIAL EQUATIONS; FINANCE; FUNCTIONS;

EULER DISCRETIZATION METHOD; HOLDER CONDITION; STOCHASTIC DRIFT TERM;

RANDOM PROCESSES;

EID: 0032026704     PISSN: 87550024     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0747(199803)14:1<77::AID-ASM338>3.0.CO;2-2     Document Type: Article

References (23)

1. J. C. Cox, J. E. Ingersoll and S. A. Ross, 'A theory of the term structure of interest rates', Econometrica, 53, 385-407 (1985).
2. G. Deelstra and F. Delbaen, 'Long-term returns in stochastic interest rate models', Insurance: Math. Econom. 17, 163-169 (1995).
3. G. Deelstra and F. Delbaen, 'Long-term returns in stochastic interest rate models: Convergence in law', Stochastics and Stochastics Reports, 55, 253-277 (1995).
4. J. Jacod, 'Une condition d'existence et d'unicité pour les solutions fortes d'équations différentielles stochastiques', Stochastics, Vol. 4, 23-28 (1980).
5. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, New York, 1988.
6. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991.
7. G. Deelstra, 'Long-term returns in stochastic interest rate models', Ph.D. thesis, Free University of Brussels, 1995.
8. I. I. Gihman and A. V. Skorohod, Stochastic differential equations, Springer, Berlin, 1972.
9. p convergence', Stochastics and Stochastics Reports, 28, 209-246 (1989).
10. V. Bally, 'Approximation of the solution of SDE's II: strong convergence', Stochastics and Stochastics Reports, 28, 357-385 (1989).
11. T. Kurtz and P. Protter, 'Wong-Zakai corrections, random evolutions, and simulation schemes for SDE's', in Stochastic Analysis, Mayer-Wolf, Merzbach, Schwarz (eds), Academic Press, New York, 1991, pp. 331-346.
12. p Stability of solutions of stochastic differential equations', Z. Wahrscheinlichkeitstheorie verw. Gebiete, 44, 337-352 (1978).
13. P. Protter, Stochastic Integration and Differential Equations, Springer, Berlin, 1990.
14. T. Yamada, 'Sur une construction des solutions d'équations différentielles stochastiques dans le cas non-Lipschitzien', in Séminaire de Probabilité XII, LNM 649, Springer, Berlin, 1978, pp. 114-131.
15. R. Bucy and P. Joseph, Filtering for Stochastic Processes with Applications to Guidance, Chelsea Publishing Company, New York, NY, 1987.
16. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992.
17. N. J. Cutland, E. Kopp and W. Willinger, 'From discrete to continuous financial models: new convergence results for option pricing', Math. Finance, 3(2), 101-123 (1993).
18. T. Kurtz and P. Protter, 'Weak limit theorems for stochastic integrals and stochastic differential equations', The Ann. Probab. 19(3), 1035-1070 (1991).
19. H. Föllmer and M. Schweizer, 'Hedging of contingent claims under incomplete information', in M. H. A. Davis and R. J. Elliott (eds), Applied Stochastic Analysis, Stochastic Monographs 5, Gordon and Breach, London, New York, 1991, pp. 389-414.
20. J. P. Ansel and C. Stricker, 'Lois de martingale, densités et décomposition de Föllmer-Schweizer', Annales de l'Institut Henri Poincaré, 28, 375-392 (1993).
21. F. Delbaen and W. Schachermayer, 'A general version of the fundamental théorem of asset pricing', Math. Ann., 300, 463-520 (1994).
22. F. Delbaen and W. Schachermayer, 'The no-arbitrage property under a change of numéraire', Stochastics and Stochastic Reports, 53, 213-226 (1995).
23. E. Wong and M. Zakai, 'On the convergence of ordinary integrals to stochastic integrals', Ann. Math. Statist., 36, 1560-1564 (1965).