VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

doi:10.1016/S0252-9602(10)60036-7

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 187-202.doi: 10.1016/S0252-9602(10)60036-7

VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

边保军, 王杨, 张寄洲

1.Department of Mathematics, Tongji University, Shanghai 200092, China |
2.Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

出版日期:2010-01-20 发布日期:2010-01-20
基金资助:
Research of this work was supported in part by National Science Foundation of China (10371088, 10671144), National Basic Research Program of China (2007CB814903), Development Funds of Shanghai Higher Education (05D210), the Special Funds for Major Specialties of Shanghai Education Committee (T0401), Supported by Special Fund for the Excellent Young Teachers of Shanghai Higher Learning Institutions (ssd08029), and the Research Program of Shanghai Normal University (SK200812).

VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

BIAN Bao-Jun, WANG Yang, ZHANG Ji-Zhou

1.Department of Mathematics, Tongji University, Shanghai 200092, China |
2.Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

Online:2010-01-20 Published:2010-01-20
Supported by:
Research of this work was supported in part by National Science Foundation of China (10371088, 10671144), National Basic Research Program of China (2007CB814903), Development Funds of Shanghai Higher Education (05D210), the Special Funds for Major Specialties of Shanghai Education Committee (T0401), Supported by Special Fund for the Excellent Young Teachers of Shanghai Higher Learning Institutions (ssd08029), and the Research Program of Shanghai Normal University (SK200812).

摘要/Abstract

摘要：

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the
European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related HJB equation are proved. A relationship between the passport and lookback options is discussed.

关键词: passport option, HJB equation, viscosity solution, uniqueness, convexity preserving

Abstract:

Key words: passport option, HJB equation, viscosity solution, uniqueness, convexity preserving

中图分类号:

91B02

边保军, 王杨, 张寄洲. VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS[J]. 数学物理学报(英文版), 2010, 30(1): 187-202.

BIAN Bao-Jun, WANG Yang, ZHANG Ji-Zhou. VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS[J]. Acta mathematica scientia,Series B, 2010, 30(1): 187-202.

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VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

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