Dynamics of Price Systems for Markets with Transaction Costs

Abstract

In a discrete time market with transaction costs, Kusuoka (1995) first gave a price formula for derivatives using preconsistent price systems (here we use the term "price system" for short). A similar result for diffusion price model was also obtained by Cvitanic-Karatzas (1996). It has been a constant interest (and also a curiosity) how such formulas can be used effectively to calculate the price of a derivative in a market with transaction costs. In this talk, a dynamic to generate the price systems will be proposed. We combine the original dynamics of stock price and the dynamics for price system to reformulate some finance problems as stochastic control problems. From this relation, dynamic programming approach can be used to study these finance problems. We will also present several preliminary results using this approach.