Sample quantiles of heavy tailed stochastic processes

Distributions of sample quantiles of measurable stochastic processes are important for the purpose of rational pricing of "look-back" options. In this paper we compute the exact tail behavior of the sample quantile distribution for a large class of infinitely divisible stochastic processes with heavy tails.

[1]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[2]  J. Akahori.  Some Formulae for a New Type of Path-Dependent Option , 1995 .

[3]  Jan Rosiński,et al.  On stochastic integral representation of stable processes with sample paths in Banach spaces , 1986 .

[4]  A. Acosta,et al.  Exponential Moments of Vector Valued Random Series and Triangular Arrays , 1980 .

[5]  Claudia Klüppelberg,et al.  Explosive Poisson shot noise processes with applications to risk reserves , 1995 .

[6]  J. Hoffmann-jorgensen,et al.  Existence of measurable modifications of stochastic processes , 1973 .

[7]  B. Rajput,et al.  Spectral representations of infinitely divisible processes , 1989 .

[8]  Werner Linde,et al.  Probability in Banach Spaces: Stable and Infinitely Divisible Distributions , 1986 .

[9]  M. Marcus.  ξ-radial processes and random Fourier series , 1987 .

[10]  Jan Rosiński,et al.  On Ito Stochastic Integration with Respect to $p$-Stable Motion: Inner Clock, Integrability of Sample Paths, Double and Multiple Integrals , 1986 .

[11]  P. Lee,et al.  14. Simulation and Chaotic Behaviour of α‐Stable Stochastic Processes , 1995 .

[12]  Jan Rosiński,et al.  On Series Representations of Infinitely Divisible Random Vectors , 1990 .

[13]  D. Aldous.  The Central Limit Theorem for Real and Banach Valued Random Variables , 1981 .

[14]  Gennady Samorodnitsky,et al.  Distributions of subadditive functionals of sample paths of infinitely divisible processes , 1993 .

[15]  Charles M. Goldie,et al.  Subexponentiality and infinite divisibility , 1979 .

[16]  S. Rachev,et al.  Modeling asset returns with alternative stable distributions , 1993 .

[17]  Ryozo Miura.  A Note on Look-Back Options Based on Order Statistics , 1992 .

[18]  M. Yor.  The distribution of Brownian quantiles , 1995 .

[19]  A. Dassios.  The Distribution of the Quantile of a Brownian Motion with Drift and the Pricing of Related Path-Dependent Options , 1995 .