A class of 𝔽-doubly stochastic markov chains

Electronic Journal of Probability

Volumn 15, Issue , 2010, Pages 1743-1771

  Jakubowski, Jacek ^a,b   Niewęgłowski, Mariusz ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Intensity; Kolmogorov equations; Martingale characterization; Predictable representation theorem; Sojourn time; doubly stochastic Markov chain

Indexed keywords

EID: 78649705567     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v15-815     Document Type: Article

References (21)

1. T. Aven. A Theorem for Determining the Compensator of a Counting Process. Scand. J. Statist. 12(1985), No. 1, 69-72.
2. D. Becherer, M. Schweizer. Classical solutions to reaction-diffusion systems for hedging problems with interacting Itô and point processes. Ann. Appl. Probab.15(2005), No. 2, 1111-1144.
3. T. Bielecki and M. Rutkowski. Credit Risk: Modeling, Valuation and Hedging. Springer Finance. Springer-Verlag Berlin Heidelberg, New York, 2001.
4. P Brémaud and M. Yor. Changes of Filtrations and of Probability Measures. Z. Wahrsch. Verw. Gebiete 45(1978), no. 4, 269-295.
5. R. Cont and P Tankov Financial modelling with jump processes. Chapman & Hall, 2004.
6. C. Dellacherie. Capacités et processus stochastiques. Springer, Berlin. (1972).
7. N. El Karoui, S. Peng, and M.C. Quenez. Backward Stochastic Differential Equations in Finance. Math. Finance 7(1997), No. 1, 1-71.
8. R.D. Gill and S. Johansen A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18(1990), No. 4, 1501-1555.
9. X. Guo and Y. Zeng Intensity Process And Compensator: A New Filtration Expansion Approach And The Jeulin-Yor Theorem. Ann. Appl. Probab. 18(2008), No. 1, 120-142.
10. Jacod, Jean and Shiryaev, Albert N. Limit theorems for stochastic processes., Grundlehren der Mathematischen Wissenschaften, 288. Springer-Verlag, Berlin, 1987.
11. J. Jakubowski and M. Nieweglowski. Pricing bonds and CDS in the model with rating migration induced by Cox process. Advances in Mathematics of Finance, ed. L. Stettner, Banach Centre Publication. 83(2008), 159-182.
12. J. Jakubowski and M. Niewqglowski. Hedging strategies of payment streams and application to defaultable rating-sensitive claims. To appear in AMaMeF volume
13. F.C. Klebaner. Introduction to stochastic calculus with applications. Second edition. Imperial College Press, London, 2005.
14. S. Kusuoka. A remark on default risk models. Adv. Math. Econ. 1(1999), 69-82.
15. H. Kunita. Ito's stochastic calculus: Its surprising power for applications Stoch. Proc. Appl. 120(2010), No. 5, 622-652.
16. D. Lando. On Cox processes and credit risky securities. Rev. Deriv. Res. 2(1998), 99-120.
17. G. Last and A. Brandt. Marked Point Processes on the Real Line: The Dynamic Approach. Springer-Verlag Berlin Heidelberg, New York, 1995.
18. E. Pardoux, and S. Peng. Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990), No. 1, 55-61.
19. P. Protter. Stochastic Integration and Differential Equations. Springer-Verlag Berlin Heidelberg, New York, 2004.
20. T. Rolski, H. Schmidli, V. Schmidt and J. Teugels. Stochastic Processes for Insurance and Finance. Wiley Series in Probability and Statistics, 1999.
21. P L. Walker. On Lebesgue Integrable Derivatives. Am. Math. Mon. 84(1977), No. 4, 287-288.