Indifference Pricing of American Option Underlying Illiquid Stock under Exponential Forward Performance
AbstractThis work focuses on the indifference pricing of American call option underlying a non-traded stock, which may be partially hedgeable by another traded stock. Under the exponential forward measure, the indifference price is formulated as a stochastic singular control problem. The value function is characterized as the unique solution of a partial differential equation in a Sobolev space. Together with some regularities and estimates of the value function, the existence of the optimal strategy is also obtained. The applications of the characterization result includes a derivation of a dual representation and the indifference pricing on employee stock option. As a byproduct, a generalized Ito's formula is obtained for functions in a Sobolev space.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1201.0075.
Date of creation: Dec 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-10 (All new papers)
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