Dynamic Asset Allocation with Stochastic Interest Rates and Transaction Costs

We investigate the optimal investment problem when the interest rate is stochastic and the investor must pay proportional transaction costs when buying and selling the risky assets. We first consider a portfolio of bonds and transaction costs.We then add a stock to the portfolio, and analyze the implications of transaction costs. To the best of our knowledge, none of these two problems has been considered in the literature before.The investor will trade less frequently when transaction costs are accounted for. This means that the optimal trading strategy is to have two boundaries for which one does not reallocate the portfolio as long as the price remains between the boundaries.Surprisingly, we find that the investor trades the bond more frequent than the stock. The reason is that the optimal invested amount in the bond depends on both the time and the maturity of the bond. We prove the existence of an upper boundary for the value function and the corresponding no-trade region. We find closed form solutions to the minimal required fluctuation of the risky assets. These minimal boundaries provides us with the optimal trading strategies. From this we find that the investor has a decreasing focus on hedging the interest rate risk with respect to time, which implies that the investor increases the amount in the bonds. This comes at the expense of reducing the amount in the stocks.In absolute terms, the increase of investments in bonds exceeds the reduction in stocks. More interestingly, we find that when the demand for long-term bonds exceeds the demand for shorter term bonds early in the investment period. The reverse is true as the investment horizon approaches