On financial markets based on telegraph processes

Stochastics

Volumn 80, Issue 2-3, 2008, Pages 247-268

  Ratanov, Nikita ^a   Melnikov, Alexander ^b  

^a UNIVERSIDAD DEL ROSARIO   (Colombia)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Black Scholes model; Hedging; Jump telegraph process; Option pricing

Indexed keywords

EID: 40249102161     PISSN: 17442508     EISSN: 17442516     Source Type: Journal    
DOI: 10.1080/17442500701841156     Document Type: Article

References (24)

1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.
2. L. Beghin, L. Nieddu, and E. Orsingher, Probabilistic analysis of the telegrapher's process with drift by mean of relativlstic transformations, J. Appl. Math. Stoch. Anal. 14 (2001), pp. 11-25.
3. P. Billingsley, Convergence of Probability Measures, John Wiley & Sons, New York, 1968.
4. T. Björk and H. Huit, A note on wick products and the fractional Black-Scholes model, Finance and Stochastics 9 (2005), pp. 197-209.
5. M.J. Brennan and E.S. Schwartz, The pricing of equity-linked life insurance policies with an asset value guarantee, J. Financ. Econ. 3 (1976), pp. 195-213.
6. A. Di Crescenzo and F. Pellerey, On prices' evolutions based on geometric telegrapher's process, Appl. Stoch. Models Bus. Industry 18 (2002), pp. 171-184.
7. G. Di Masi, Y. Kabanov, and W. Runggaldier, Mean-variance hedging of options on stocks with Markov volatilities, Theory Probab. Appl. 39 (1994), pp. 172-182.
8. F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing, Mathematiche Annalen 300 (1994), pp. 463-520.
9. D. Duffle, Dynamic Asset Pricing Theory, Princeton University Press, Princeton, 1996.
10. R. Elliott and J. van der Hoek, An application of hidden Markov models to asset allocation problems, Finance and Stochastics 1 (1997), pp. 229-238.
11. H. Föllmer and P. Leukert, Quantile hedging, Finance and Stochastics 3 (1999), pp. 251-273.
12. _, Efficient hedging: Cost versus shortfall risk, Finance and Stochastics 4 (2000), pp. 117-146.
13. S. Goldstein, On diffusion by discontinuous movements and on the telegraph equation, Quart. J. Mech. Appl. Math. 4 (1951), pp.129-156.
14. M. Kac, Probability and Related Topics in Physical Sciences, Interscience, London, 1959.
15. _, A stochastic model related to the telegraph equation, Rocky Mountain J. Math. 4 (1974), pp. 497-509.
16. I. Karatzas and S. E. Shreve, Methods of Mathematical Finance, vol. 39 of Applications of Mathematics, Springer-Verlag, New York, 1998.
17. A. Melnikov, S. Volkov, and M. Nechaev, Mathematics of Financial Obligations. (Translations of Mathematical Monographs. 212. Providence, RI: American Mathematical Society, ix, 194 p), 2002.
18. R. C. Merton, Coninuous-Time Finance, Blackwell, Oxford, 1990.
19. E. Orsingher, Probability law, flow function, maximum distribution of wave-governed random motions and their connection with Kirchhoff's law, Stoch. Process. Appl. 38 (1990), pp. 49-66.
20. _, Motions with reflecting and absorbing barriers driven by the telegraph equation, Random Oper. Stochast. Equ. 3 (1995), pp. 9-21.
21. N. Ratanov, Telegraph evolutions in inhomogeneous media, Markov Processes Relat. Rields 5 (1999), pp. 53-68.
22. _, A jump telegraph model for option pricing, Quant. Finance 7(5) (2007), pp. 575-583.
23. S. M. Ross, Stochastic Processes, John Willey & Sons, New York, 1983.
24. S. Zacks, Generalized integrated telegraph processes and the distribution of related stopping times, J. Appl. Prob. 41 (2004), pp. 497-507.