Department of Mathematical SciencesIn this paper, we will investigate optimal investment and consumption strategies in the market with CRRA utility function. In this market, the investor chooses a portfolio that consists of one bond (with zero interest rates), one illiquid risky asset (having transaction costs), and one liquid risky asset (having no transaction costs). Using shadow price which is the virtual price between the bid and ask price, we can derive the optimal investment and consumption strategies. From these results we obtained, we will apply to the market having stock and residential real estate. For the analyze, we chose KOSPI200 (the index consists of 200 big companies
of the Stock Market Division in Korea) for the stock and house price index (the price of the residential real estate in Korea) for the real estate. With KOSPI200 and house price index data, we obtained the optimal investment and consumption strategies and also checked the effect of the transaction costs on two risky assets and consumption.clos
