Article history: Received 1 August 2012 Received in revised form 26 September 2013 Accepted 3 November 2013 Available online xxxx While stock options are commonly used in managerial compensation to provide desirable incentives, they can create adverse incentives to distort the choice of investment risk. Relative to the risk level that maximizes firm value, call options in a compensation contrac...

In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff (y − x)+ is replaced by φ(x, y). It turns out that the duality still holds under monotonicity and concavity assumptions on φ. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the d...