Exact Monte Carlo simulation of killed diffusions

Advances in Applied Probability

Volumn 40, Issue 1, 2008, Pages 273-291

  Casella, Bruno ^a   Roberts, Gareth O ^b  

^a University of Warwick ^*  (Italy)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Diffusions; Exact algorithm; Monte Carlo

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; MATHEMATICAL MODELS; MONTE CARLO METHODS; ONE DIMENSIONAL;

EXACT ALGORITHM; EXACT MONTE CARLO SIMULATION; KILLED DIFFUSIONS; MONTE CARLO ALGORITHM;

DIFFUSION;

EID: 44649193848     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1208358896     Document Type: Article

References (22)

1. ANDERSON, T. W. (1960). A modification of the sequential probability ratio test to reduce the sample size. Ann. Math. Statist. 31, 165-197.
2. ASMUSSEN, S. AND GLYNN, P. W. (2007). Stochastic Simulation: Algorithms and Analysis. Springer, New York.
3. BERTOIN, J. AND PITMAN, J. (1994). Path transformations connecting Brownian bridge, excursion and meander. Bull. Sci. Math. 118, 147-166.
4. BESKOS, A. AND ROBERTS, G. O. (2005). Exact simulation of diffusions. Ann. Appl. Prob. 15, 2422-2444.
5. BESKOS, A. AND PAPASPILIOPOULOS, O. AND ROBERTS, G. O. (2006a). Retrospective exact simulation of diffusion sample paths with applications. Bernoulli 12, 1077-1098.
6. BESKOS, A. AND PAPASPILIOPOULOS, O. AND ROBERTS, G. O. (2008). A new factorisation of diffusion measure and sample path reconstruction. To appear in Methodology Comput. Appl. Prob..
7. BESKOS,A. AND PAPASPILIOPOULOS, O. AND ROBERTS, G. O. AND FEARNHEAD, P. (2006b). Exact and efficient likelihood based inference for discretely observed diffusions (with discussion). J. R. Statist. Soc. B 68, 333-382.
8. BLACK, F. AND COX, J. C. (1976). Valuing corporate securities: some effects of bond indenture provisions. J. Finance 31, 351-367.
9. BOSSY, M., GOBET, E. AND TALAY, D. (2004). A symmetrized Euler scheme for an efficient approximation of reflected diffusions. J. Appl. Prob. 41, 877-889.
10. DAVYDOV, D. AND LINETSKY, V. (2001). The valuation and hedging of barrier and lookback options under the CEV process. Manag. Sci. 47, 949-965.
11. DEVROYE, L. (1986). Nonuniform Random Variate Generation. Springer, New York.
12. DOOB, J. L. (1949). Heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Statist. 20, 393-403.
13. FEARNHEAD, P., PAPASPILIOPOULOS, O. AND ROBERTS, G. O. (2008). Particle filters for partially observed diffusions. To appear in J. R. Statist. Soc. B.
14. GOBET, E. (2000). Weak approximation of killed diffusion using Euler schemes. Stoch. Process. Appl. 87, 167-197.
15. GOBET, E. (2001). Euler schemes and half-space approximation for the simulation of diffusion in a domain. ESAIM Prob. Statist. 5, 261-297.
16. LÉPINGLE, D. (1995). Euler scheme for reflected stochastic differential equations. Math. Comput. Simad. 38, 119-126.
17. LERCHE, H. R. (1986). Boundary Crossing of Brownian Motion. (Lecture Notes Statist. 40). Springer Berlin.
18. LONGSTAFF, F. A. AND SCHWARZ, E. S. (1995). A simple approach to valuing risky and floating rate debt. J. Finance 50, 789-819.
19. MERTON, R. C. (1971). Theory of rational option pricing. Bell J. Econom. Manag. 4, 141-183.
20. ØKSENDAL, B. K. (1998). Stochastic Differential Equations. An Introduction with Applications, 5th edn. Springer, Berlin.
21. PÖTZELBERGER, K. AND WANG, L. (2001). Boundary crossing probability for Brownian motion. J. Appl. Prob. 38, 152-164.
22. REINER, E. AND RUBINSTEIN, M. (1991). Breaking down the barriers. Risk 4, 28-35.