Indifference pricing and hedging in a multiple-priors model with trading constraints

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• 作者：HuiWen Yan (1)
  GeChun Liang (2)
  Zhou Yang (3)
  
  1. School of Mathematics and Statistics ; Guangdong University of Finance and Economics ; Guangzhou ; 510320 ; China
  2. Department of Mathematics ; King鈥檚 College London ; London ; WC2R 2LS ; UK
  3. School of Mathematical Sciences ; South China Normal University ; Guangzhou ; 510631 ; China
  
• 关键词：indifference pricing ; stochastic differential utility ; trading constraints ; ambiguity ; variational inequality ; American option ; 35K86 ; 35Q91 ; 35Q93 ; 49N90 ; 60H10
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：58
• 期：4
• 页码：689-714
• 全文大小：344 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein (2002). The price is determined by two optimal stochastic control problems (mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations. By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates. The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.