A REMARK ON THE HEAT EQUATION WITH A POINT PERTURBATION, THE FEYNMAN-KAC FORMULA WITH LOCAL TIME AND DERIVATIVE PRICING

被引：1

作者：

Albeverio, Sergio ^{[1
,2
,3
]}

Fassari, Silvestro ^{[2
,4
,5
]}

Rinaldi, Fabio ^{[2
,5
,6
]}

机构：

[1] Univ Bonn, Inst Angew Math, HCM, IZKS,BiBoS, D-53115 Bonn, Germany

[2] CERFIM, CH-6601 Locarno, Switzerland

[3] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[4] ISR, CH-9470 Buchs, Switzerland

[5] Univ Guglielmo Marconi, I-00193 Rome, Italy

[6] Punjab Tech Univ, BIS Grp Inst, Gagra Moga, Punjab, India

来源：

REPORTS ON MATHEMATICAL PHYSICS | 2015年 / 75卷 / 02期

关键词：

point interactions; heat equation; heat kernel; Feynman-Kac formula; Brownian motion; local time; option pricing; Black-Scholes equation;

D O I：

10.1016/S0034-4877(15)30006-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman-Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black-Scholes options and knockouts having the barrier situated exactly at the exercise price.

引用

页码：257 / 265

页数：9

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