Economy – Quantitative Finance – Pricing of Securities
Scientific paper
2011-12-30
Economy
Quantitative Finance
Pricing of Securities
23 pages
Scientific paper
This 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.
Chen Xiaoshan
Song Qingshuo
Yi Fahuai
Yin George G.
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