The Bermudan option pricing problem with variable transaction costs is
considered for a risky asset whose price process is derived under
the information-based model. The price is formulated as the value
function of an optimal stopping problem, which is the value function of a
stochastic control problem given by a non-linear second order partial
differential equation. The theory of viscosity solutions is applied to solve
the stochastic control problem such that the value function is also the
solution of the corresponding Bellman equation. Under some regularity
assumptions, the existence and uniqueness of the solution of the pricing
equation are derived by the application of the Perron method and Banach Fixed
Point theorem.
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