Investors' preference for a positive tax rate depends on the level of the interest rate (Q926393)

The authors study a financial market in which there are transaction costs proportional to the current portfolio value and taxes on the income generated by the portfolio. This model has been studied by the authors before, but in a less general set-up. Here, the authors consider many risky assets and a positive interest rate. The main economic insight is -- as in the previous literature -- that a positive tax rate can be interesting for investors interested in the long run growth rate of their portfolios. The economic reason for this is that the positive tax rates provide a cushion against potential losses or the utility of the risky assets. The main contribution of the current paper is therefore technical. In a first step the authors show how to reduce the problem to a context of a renewal theory where we face essentially a sequence of identically distributed and independent random variables. The problem of finding an optimal strategy in this transaction cost set-up as then reduced to one optimal stopping problem. The authors then use the numerical method, in particular the Markov chain approximation, to show that the positive interest rate can matter in general.