Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences

Analytic bounds on the reservation write price of European-style contingent claims are derived in the presence of proportional transaction costs in a model which allows for intermediate trading. The option prices are obtained via a utility maximization approach by comparing the maximized utilities with and without the contingent claim. The mathematical tools come mainly from the theories of singular stochastic control and viscosity solutions of nonlinear partial differential equations.