Polynomial processes and their applications to mathematical finance

Finance and Stochastics

Volumn 16, Issue 4, 2012, Pages 711-740

  Cuchiero, Christa ^a   Keller Ressel, Martin ^b   Teichmann, Josef ^c  

^a UNIVERSITY OF VIENNA   (Austria)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c ETH ZURICH   (Switzerland)

Author keywords

Affine processes; Analytic tractability; Diffusions with jumps; Hedging; Markov processes; Pricing

Indexed keywords

EID: 84866272069     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-012-0188-x     Document Type: Article

References (23)

1. Akhiezer, N. I.: The Classical Moment Problem and Some Related Questions in Analysis. Hafner Publishing Co., New York (1965). Translated by N. Kemmer.
2. Bates, D. S.: Post-'87 crash fears in the S& P 500 futures option market. J. Econom. 94, 181-238 (2000).
3. Carr, P., Madan, D.: Option valuation using the fast Fourier transform. J. Comput. Finance 2, 61-73 (1998).
4. Chen, L., Filipović, D., Poor, H. V.: Quadratic term structure models for risk-free and defaultable rates. Math. Finance 14, 515-536 (2004).
5. Cheridito, P., Filipović, D., Yor, M.: Equivalent and absolutely continuous measure changes for jump-diffusion processes. Ann. Appl. Probab. 15, 1713-1732 (2005).
6. Çinlar, E., Jacod, J., Protter, P., Sharpe, M. J.: Semimartingales and Markov processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 161-219 (1980).
7. Duffie, D., Filipović, D., Schachermayer, W.: Affine processes and applications in finance. Ann. Appl. Probab. 13, 984-1053 (2003).
8. Dunkl, C. F.: Hankel transforms associated to finite reflection groups. In: Beals, R. W. (ed.) Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, Tampa, FL, 1991. Contemp. Math., vol. 138, pp. 123-138. Amer. Math. Soc., Providence (1992).
9. Engel, K.-J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics, vol. 194. Springer, New York (2000). With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli, R. Schnaubelt.
10. Forman, J. L., Sørensen, M.: The Pearson diffusions: A class of statistically tractable diffusion processes. Scand. J. Stat. 35, 438-465 (2008).
11. Gallardo, L., Yor, M.: Some remarkable properties of the Dunkl martingales. In: Emery, M., Yor, M. (eds.) In memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX. Lecture Notes in Math., vol. 1874, pp. 337-356. Springer, Berlin (2006).
12. Gatheral, J.: The Volatility Surface: A Practitioner's Guide. Wiley Finance (2006).
13. Golub, G. H., van Loan, C. F.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences, 3rd edn. Johns Hopkins University Press, Baltimore (1996).
14. Gourieroux, C., Jasiak, J.: Multivariate Jacobi process with application to smooth transitions. J. Econom. 131, 475-505 (2006).
15. Jacod, J., Shiryaev, A. N.: Limit Theorems for Stochastic Processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 288. Springer, Berlin (1987).
16. Jacod, J., Kurtz, T. G., Méléard, S., Protter, P.: The approximate Euler method for Lévy driven stochastic differential equations. Ann. Inst. Henri Poincaré Probab. Stat. 41, 523-558 (2005).
17. Keller-Ressel, M., Schachermayer, W., Teichmann, J.: Affine processes are regular. Probab. Theory Relat. Fields 151, 591-611 (2011).
18. Kunita, H.: Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms. In: Real and Stochastic Analysis. Trends Math., pp. 305-373. Birkhäuser, Boston (2004).
19. Moler, C., van Loan, C.: Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 20, 801-836 (1978).
20. Reed, M., Simon, B.: Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness. Academic Press [Harcourt Brace Jovanovich Publishers], New York (1975).
21. Reimer, M.: Multivariate Polynomial Approximation. International Series of Numerical Mathematics, vol. 144. Birkhäuser, Basel (2003).
22. Rogers, L. C. G., Williams, D.: Diffusions, Markov Processes, and Martingales. Vol. 1 Foundations. Cambridge Mathematical Library. Cambridge University Press, Cambridge (2000). Reprint of the second (1994) edition.
23. Zhou, H.: Itô conditional moment generator and the estimation of short rate processes. J. Financ. Econom. 1, 250-271 (2003).