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

• Published in: Acta mathematica scientia Vol. 30; no. 1; pp. 187 - 202
• Main Author: 边保军 王杨 张寄洲
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2010; Department of Mathematics, Tongji University, Shanghai 200092, China%Department of Mathematics, Tongji University, Shanghai 200092, China; Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China%Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
• Subjects: 35B05; 49L25; 91B02; convexity preserving; Foundations; Gain; HJB equation; HJB方程; Mathematical analysis; Nonlinear equations; passport option; Passports; Pricing; Uniqueness; Viscosity; viscosity solution; 数学基础; 期权定价; 非线性方程; viscosity solution; 35B05; convexity preserving; uniqueness; HJB equation; 91B02; passport option; 49L25
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(10)60036-7

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 H J13 equation are proved. A relationship between the passport and lookback options is discussed.