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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:

2015年04期

Page:

71-

Research Field:

数学

Publishing date:

Info

Title:

An American Call Option Pricing Model for Risk-Averse Invertors

Author(s):

Cen Yuanjun¹; Yi Fahuai²

（1.Section of Higher Vocational Mathematics，Shunde Polytechnic，Foshan 528333，China）（2.School of Mathematics，South China Normal University，Guangzhou 510631，China）

Keywords:

the standard American options; option pricing; optimal exercise boundary

PACS:

O175.26

DOI:

-

Abstract:

There is a new American call option which is designed for risk-averse invertors. The mathematical pricing model of this option can be formulated as a one-dimensional parabolic variational inequality，or equivalently，a free boundary problem. Different from the standard American call，it has two monotonous smooth free boundaries with dividends and has only one linear free boundary without dividends. To solve this problem，PDE arguments are applied. We can prove the existence and uniqueness of the solution. Then the properties of the free boundaries，such as monotonicity，smoothness，and location，are presented.

References:

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［3］GUO X，SHEPP L. Some optimal stopping problems with nontrival boundaries for pricing exotic options［J］. Appl Prob，2001，38：647-658.
［4］JIANG L S. Mathematical modeling and methods of option pricing［M］. Singapore：World Scientific，2005.
［5］AVNER FRIEDMAN. Variational principle and free boundary problems［M］. New York：John Wiley & Sons，1982.
［6］陈亚浙. 二阶抛物型偏微分方程［M］. 北京：北京大学出版社，2003.
［7］CONNON J R，HENRY D B，KOTLOV D B. Continuous differentiability of the free boundary for weak solutions of the Stefan problem［J］. Bull Ane Math Soc，1974，80：45-48.
［8］FRIEDMAN A. Parabolic variational inequalities in one space dimension and smoothness of the free boundary［J］. J?Funct Anal，1975，18：151-176.

Memo

Memo:

-

Common functions

Last Update: 2015-12-30