THE PORTFOLIO PROBLEM UNDER THE VARIABLE RATE OF TRANSACTION COSTS

Chunfang Yang (P. R. China) and Peibiao Zhao (P. R. China)

Received January 23, 2008

Abstract

In the frictional market, contingent claims usually cannot be completely hedged, and this hedging problem can be regarded as a portfolio problem. Recently, people are studying the portfolio problem under the frictional market, but just studying the problem of the fixed rate of transaction costs. As far as we know, the research about the variable rate is still open. This paper poses a jump rate of transaction costs according to the real market, and based on this, we get an optimal model of minimizing risk. For this model, we use the Calculus of Variation to prove the existence of the optimal strategy.

Keywords and phrases: portfolio, rate of transaction costs, jump model.