APPROXIMATING LEVY PROCESSES WITH COMPLETELY MONOTONE JUMPS

被引：11
|
作者：
Hackmann, Daniel [1 ]
Kuznetsov, Alexey [1 ]
机构：
[1] York Univ, Dept Math & Stat, 4700 Keele St, Toronto, ON M3J 1P3, Canada
来源：
ANNALS OF APPLIED PROBABILITY | 2016年 / 26卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Levy processes; complete monotonicity; hyperexponential processes; Pade approximation; rational interpolation; Gaussian quadrature; Stieltjes functions; Jacobi polynomials; WIENER-HOPF FACTORIZATION; ASIAN OPTIONS; BARRIER; STIELTJES; DRIVEN; PRICES; FAMILY;
D O I：
10.1214/14-AAP1093
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Levy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on Levy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse Gaussian) belong to this class. In this paper we continue the work started in [Int. J. Theor. Appl. Finance 13 (2010) 63-91, Quant. Finance 10 (2010) 629-644] and develop a simple yet very efficient method for approximating processes with completely monotone jumps by processes with hyperexponential jumps, the latter being the most convenient class for performing numerical computations. Our approach is based on connecting Levy processes with completely monotone jumps with several areas of classical analysis, including Pade approximations, Gaussian quadrature and orthogonal polynomials.
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页码：328 / 359
页数：32
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