Abstract
For wide classes of put-like and call-like perpetual options under Levy processes satisfying the (ACP)-property, the optimal exercise price and rational option price are found. The results are formulated in terms of resolvent operators of the supremum and infimum processes, which are natural generalization of resolvent operators in the Markovian case, and a short proof of optimality based on properties of these resolvents is given. As an application, the problem of incremental capital expansion is solved.
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