Analysis of market weights under volatility-stabilized market models

Annals of Applied Probability

Volumn 21, Issue 3, 2011, Pages 1180-1213

  Pal, Soumik ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Bessel processes; Kelvin transform; Market weights; Volatility stabilized markets; Wright Fisher model

Indexed keywords

EID: 79958209387     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/10-AAP725     Document Type: Article

References (30)

1. AXLER, S., BOURDON, P. and RAMEY, W. (2001). Harmonic Function Theory, 2nd ed. Graduate Texts in Mathematics 137. Springer, New York. MR1805196
2. BASS, R. F. and PERKINS, E. A. (2003). Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains. Trans. Amer. Math. Soc. 355 373-405 (electronic). MR1928092 (Pubitemid 36116505)
3. BORODIN, A. N. and SALMINEN, P. (2002). Handbook of Brownian Motion-Facts and Formulae, 2nd ed. Probability and Its Applications. Birkhäuser, Basel. MR1912205
4. BRU, M.-F. (1991). Wishart processes. J. Theoret. Probab. 4 725-751. MR1132135
5. CARMONA, P., PETIT, F. and YOR, M. (2001). Exponential functionals of Lévy processes. In Lévy Processes (O. E. Barndorff-Nielson, T. Mikosch and S. I. Resnick, eds.) 41-55. Birkhäuser, Boston, MA. MR1833691
6. CHATTERJEE, S. and PAL, S. (2010). A phase transition behavior for Brownian motions interacting through their ranks. Probab. Theory Related Fields 147 123-159. MR2594349
7. COX, J. C., INGERSOLL JR., J. E. and ROSS, S. A. (1985). A theory of the term structure of interest rates. Econometrica 53 385-407. MR0785475
8. DURRETT, R. (2008). Probability Models for DNA Sequence Evolution, 2nd ed. Probability and Its Applications (New York). Springer, New York. MR2439767
9. EISENBAUM, N. (1994). Dynkin's isomorphism theorem and the Ray-Knight theorems. Probab. Theory Related Fields 99 321-335. MR1278888
10. ETHERIDGE, A. M. (2000). An Introduction to Superprocesses. University Lecture Series 20. Amer. Math. Soc., Providence, RI. MR1779100
11. ETHIER, S. N. and KURTZ, T. G. (1981). The infinitely-many-neutral- alleles diffusion model. Adv. in Appl. Probab. 13 429-452. MR0615945
12. ETHIER, S. N. and KURTZ, T. G. (1993). Fleming-Viot processes in population genetics. SIAM J. Control Optim. 31 345-386. MR1205982 (Pubitemid 23641393)
13. FERNHOLZ, E. R. and KARATZAS, I. K. (2005). Relative arbitrage in volatility-stabilized markets. Ann. Finan. 1 149-177.
14. FERNHOLZ, R. and KARATZAS, I. (2009). Stochastic portfolio theory: An overview. In Handbook of Numerical Analysis (P. G. Ciarlet, ed.) XV. Special Volume: Mathematical Modelling and Numerical Methods in Finance (A. Bensoussan Q. Zhang, Guest eds.) 89-168. Elsevier, Amsterdam.
15. GEMAN, H. and YOR, M. (1993). Bessel processes, Asian options, and perpetuities. Math. Finance 3 349-375.
16. GOIA, I. (2009). Bessel and volatility-stabilized processes. Ph.D. thesis, Columbia Univ.
17. GRIFFITHS, R. C. (1979). On the distribution of allele frequencies in a diffusion model. Theoret. Population Biol. 15 140-158. MR0528914
18. GRIFFITHS, R. C. (1979). A transition density expansion for a multi-allele diffusion model. Adv. in Appl. Probab. 11 310-325. MR0526415
19. HASHEMI, F. (2000). An evolutionary model of the size distribution of firms. J. Evol. Econ. 10 507-521.
20. IJIRI, Y. and SIMON, H. (1977). Interpretations of departures from the Pareto curve firm-size distributions. Journal of Political Economy 82 315-331.
21. JOVANOVIC, B. (1982). Selection and the evolution of industry. Econometrica 50 649-670. MR0662724
22. KÖNIG, W. andO'CONNELL, N. (2001). Eigenvalues of the Laguerre process as non-colliding squared Bessel processes. Electron. Comm. Probab. 6 107-114 (electronic). MR1871699 (Pubitemid 38818002)
23. PITMAN, J. (1996). Cyclically stationary Brownian local time processes. Probab. Theory Related Fields 106 299-329. MR1418842 (Pubitemid 126354539)
24. PITMAN, J. and YOR, M. (1982). A decomposition of Bessel bridges. Z. Wahrsch. Verw. Gebiete 59 425-457. MR0656509
25. REVUZ, D. and YOR, M. (1999). Continuous Martingales and Brownian Motion, 3rd ed. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 293. Springer, Berlin. MR1725357
26. SHIGA, T. andWATANABE, S. (1973). Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrsch. Verw. Gebiete 27 37-46. MR0368192
27. SIMON, H. and BONINI, C. (1955). The size distribution of business firms. Amer. Econ. Rev. 48 607-617.
28. TAVARÉ, S. (1984). Line-of-descent and genealogical processes, and their applications in population genetics models. Theoret. Population Biol. 26 119-164. MR0770050
29. WARREN, J. and YOR, M. (1998). The Brownian burglar: Conditioning Brownian motion by its local time process. In Séminaire de Probabilités, XXXII. Lecture Notes in Math. 1686 328-342. Springer, Berlin. MR1655303
30. WERNER, W. (1995). Some remarks on perturbed reflecting Brownian motion. In Séminaire de Probabilités, XXIX. Lecture Notes in Math. 1613 37-43. Springer, Berlin. MR1459447