Relative arbitrage in volatility-stabilized markets

Annals of Finance

Volumn 1, Issue 2, 2005, Pages 149-177

  Fernholz, Robert ^a   Karatzas, Ioannis ^b  

^a INTECH   (United States)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Bessel processes; Diversity; Portfolios; Relative arbitrage; Stochastic differential equations; Strict local martingales; Time change; Volatility stabilized markets

Indexed keywords

EID: 13444254352     PISSN: 16142446     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10436-004-0011-6     Document Type: Article

References (16)

1. Banner, A., Fernholz, R., Karatzas, I.: On Atlas models of equity markets. Preprint (2004)
2. Bass, R., Perkins, E.: Degenerate stochastic differential equations with Hölder-continuous coëfficients and super-Markov chains. Transactions of the American Mathematical Society 355, 373-405 (2002)
3. Cherny, A.S.: Convergence of some integrals associated with Bessel processes. Theory of Probability and Its Applications 45, 195-209 (2000)
4. Fernholz, E.R.: Stochastic portfolio theory. Berlin Heidelberg New York: Springer 2002
5. Fernholz, R., Karatzas, I., Kardaras, C.: Diversity and relative arbitrage in equity markets. Finance & Stochastics 9, 1-27 (2005)
6. + and their Lamperti representations. Probability Theory and Related Fields 126, 1-28 (2003)
7. Kallianpur, G., Robbins, H.: Ergodic property of the planar Brownian motion process. Proceedings of the National Academy of Sciences 39, 525-533 (1953)
8. Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus. 2nd edn. Berlin Heidelberg New York: Springer 1991
9. Karatzas, I., Shreve, S.E.: Methods of mathematical finance. Berlin Heidelberg New York: Springer 1998
10. Pitman, J., Yor, M.: Asymptotic laws for planar Brownian motion. Annals of Probability 14, 733-779 (1986)
11. Pitman, J., Yor, M.: Some divergent integrals of Brownian motion. In: Kendall, D. (ed.) Analysis and geometric stochastics. In honor of G.H. Reuter. Advances in Applied Probability (Suppl.) 18, 109-116 (1986a)
12. Pitman, J., Yor, M.: Further asymptotic laws for planar Brownian motion. Annals of Probability 17, 965-1011 (1989)
13. Spitzer, F.: Some theorems concerning two-dimensional Brownian motion. Transactions of the American Mathematical Society 87, 187-197 (1958)
14. n Lecture Notes in Mathematics 1204, 543-552 (1985)
15. Yor, M.: Sur certaines functionelles exponentielles du mouvement Brownien. Journal of Applied Probability 29, 202-208 (1992)
16. Yor, M.: Personal Communication (2004)