Time-homogeneous diffusions with a given marginal at a random time

ESAIM - Probability and Statistics

Volumn 15, Issue , 2011, Pages S11-S24

  Cox, Alexander M G ^a   Hobson, David ^b   Oblój, Jan ^c  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Bertoin Le Jan stopping time; Exponential time; Generalised diffusion; Skorokhod embedding problem; Time homogeneous diffusion

Indexed keywords

EMBEDDING PROBLEMS; EXPONENTIAL TIME; FOLLOWING PROBLEM; LINEAR DIFFUSION; PROBABILITY MEASURES; SPECTRAL THEORY; STOPPING TIME;

STATISTICS;

DIFFUSION;

EID: 84855678731     PISSN: 12928100     EISSN: 12623318     Source Type: Journal    
DOI: 10.1051/ps/2010021     Document Type: Article

References (20)

1. J. Bertoin and Y. Le Jan, Representation of measures by balayage from a regular recurrent point. Ann. Probab. 20 (1992) 538-548.
2. P. Carr, Local Variance Gamma. Private communication (2008).
3. P. Carr and D. Madan, Determining volatility surfaces and option values from an implied volatility smile, in Quantitative Analysis of Financial Markets II, edited by M. Avellaneda. World Scientific (1998) 163-191.
4. R.V. Chacon, Potential processes. Trans. Amer. Math. Soc. 226 (1977) 39-58.
5. A.M.G. Cox, Extending Chacon-Walsh: Minimality and generalised starting distributions, in Séminaire de Probabilités XLI. Lecture Notes in Math. 1934, Springer, Berlin (2008) 233-264.
6. J.L. Doob, Measure theory. Graduate Texts Math. 143, Springer-Verlag, New York (1994).
7. B. Dupire, Pricing with a smile. Risk 7 (1994) 18-20.
8. H. Dym and H.P. McKean, Gaussian processes, function theory, and the inverse spectral problem. Probab. Math. Statist. 31. Academic Press (Harcourt Brace Jovanovich Publishers), New York (1976).
9. D. Hobson, The Skorokhod Embedding Problem and Model-Independent Bounds for Option Prices, in Paris-Princeton Lectures on Mathematical Finance 2010, edited by R.A. Carmona, E. Cinlar, I. Ekeland, E. Jouini, J.A. Scheinkman and N. Touzi. Lecture Notes in Math. 2003, Springer (2010) 267-318. www.warwick.ac.uk/go/dhobson/
10. K. Ito, Essentials of stochastic processes. Translations Math. Monographs 231, American Mathematical Society, Providence, RI, (2006), translated from the 1957 Japanese original by Yuji Ito.
11. L. Jiang and Y. Tao, Identifying the volatility of underlying assets from option prices. Inverse Problems 17 (2001) 137-155.
12. I.S. Kac and M.G. Krein, Criteria for the discreteness of the spectrum of a singular string. Izv. Vyss. Ucebn. Zaved. Matematika 2 (1958) 136-153.
13. F.B. Knight, Characterization of the Levy measures of inverse local times of gap diffusion, in Seminar on Stochastic Processes (Evanston, Ill., 1981). Progr. Probab. Statist. 1, Birkhauser Boston, Mass. (1981) 53-78.
14. S. Kotani and S. Watanabe, Krein’s spectral theory of strings and generalized diffusion processes, in Functional analysis in Markov processes (Katata/Kyoto, 1981). Lecture Notes in Math. 923, Springer, Berlin (1982) 235-259.
15. M.G. Krein, On a generalization of investigations of Stieltjes. Doklady Akad. Nauk SSSR (N.S.) 87 (1952) 881-884.
16. U. Kiichler and P. Salminen, On spectral measures of strings and excursions of quasi diffusions, in Séminaire de Probabilités XXIII. Lecture Notes in Math. 1372, Springer, Berlin (1989) 490-502.
17. D.B. Madan and M. Yor, Making Markov martingales meet marginals: With explicit constructions. Bernoulli 8 (2002) 509-536.
18. I. Monroe, On embedding right continuous martingales in Brownian motion. Ann. Math. Statist. 43 (1972) 1293-1311.
19. J. Obloj, The Skorokhod embedding problem and its offspring. Prob. Surveys 1 (2004) 321-392.
20. L.C.G. Rogers and D. Williams, Diffusions, Markov processes, and martingales, volume 2, Ito Calculus. Cambridge University Press, Cambridge, reprint of the second edition of 1994 (2000).