Free Boundary Problems in Asset Pricing with Transaction Costs
This presentation provides an overview of a class of free boundary problems that arise in valuation models in markets with transaction costs. Transaction costs are a realistic feature in numerous financial transactions and their presence affects considerably the theoretical asset and derivative prices.
In the area of optimal portfolio management, the valuation models give rise to singular stochastic control problems and the goal is to characterize the value function (maximal utility) and to specify the optimal control policies.
In the area of derivative pricing, the classical Black and Scholes valuation theory, based on exact replication, breaks down completely when transaction costs are present. Various approaches have been developed which lead to free boundary problems for the derivative prices. These methods include among others, the method of super-replicating strategies and the utility maximization theory.
KeywordsTransaction Cost Asset Price Viscosity Solution Portfolio Selection Free Boundary Problem
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