Some remarks on first passage of Levy processes, the American put and pasting principles

被引：119

作者：

Alili, L ^{[1
]}

Kyprianou, AE

机构：

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[2] Univ Utrecht, NL-3500 TA Utrecht, Netherlands

来源：

ANNALS OF APPLIED PROBABILITY | 2005年 / 15卷 / 03期

关键词：

optimal stopping; American options; principle of smooth pasting; principle of continuous pasting; Levy processes;

D O I：

10.1214/105051605000000377

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：

The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J Control Optim. 40 (2002) 1663-1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process. Appl. 100 (2002) 75-107], Mordecki [Finance Stoch. 6 (2002) 473-493], Asmussen, Avram and Pistorius [Stochastic Process. Appl. 109 (2004) 79-111] and Chesney and Jeanblanc [Appl. Math. Fin. 11 (2004) 207-225] to the American perpetual put optimal stopping problem. Furthermore, we make folklore precise and give necessary and sufficient conditions for smooth pasting to occur in the considered problem.

引用

页码：2062 / 2080

页数：19

共 37 条

[1]

Almendral A., 2005, EXOTIC OPTION PRICIN

[2]

ALMENDRAL A, 2003, AM OPTIONS VARIANCE

[3]

[Anonymous], 2002, Advances in Finance and Statistics, Essays in Honour of Dieter Sondermann and P. Schonbucher

[4] Russian and American put options under exponential phase-type Levy models [J].

Asmussen, S ;

Avram, F ;

Pistorius, MR .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 109 (01) :79-111

[5]

Asmussen S., 2000, Ruin probabilities

[6]

Avram F, 2004, ANN APPL PROBAB, V14, P215

[7] On the valuation of constant barrier options under spectrally one-sided exponential Levy models and Carr's approximation for American puts [J].

Avram, F ;

Chan, T ;

Usabel, M .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 100 :75-107

[8]

Bertoin J, 1997, B SCI MATH, V121, P345

[9]

Bertoin J., 1996, Levy Processes

[10]

Bertoin J, 1997, ANN APPL PROBAB, V7, P156

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