Acta mathematica scientia, Series B >
VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS
Online 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).
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.
Key words： passport option; HJB equation; viscosity solution; uniqueness; convexity preserving
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 . DOI: 10.1016/S0252-9602(10)60036-7
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