The problem of the portfolio demand for money was first rigorously studied by Tobin [22]. It has been analyzed since then, by Hicks [8] and Arrow [1], among many others. Many interesting results and implications regarding liquidity preference and risk-taking are derived in these studies. However, the effect of purchasing power risk on liquidity preference has been overlooked in these studies.

We have formulated the mean-variance models of portfolio selection with stochastic cash demand. The results of the general model have indicated that the characteristic of the investor's stochastic cash demand, the liquidity risks of assets (measured by the covariance between an asset's return and the cash demand), and the structure of transfer costs also play important roles in the determination of the investor's optimal portfolio. We have also shown that the model of portfolio selection with stochastic cash demand can be greatly simplified if the assumption of symmetric transfer costs is invoked. Furthermore, it has been shown that the simplified model can be reformulated and solved by the LP techniques. Thus, LP formulation of portfolio selection with stochastic cash demand should have practical usefulness.Finally, along the line of works by Chen, Jen and Zionts [3, 4], Pogue [14, 15] and Stone and Reback [20], one can extend the analysis in this paper to the problem of dynamic portfolio management with stochastic cash demand and transfer costs.

Andrew H. Chen, External Financing and Liquidity: Discussion, The Journal of Finance, Vol. 39, No. 3, Papers and Proceedings, Forty-Second Annual Meeting, American Finance Association, San Francisco, CA, December 28-30, 1983 (Jul., 1984), pp. 908-910

Over the last decade, there has been considerable public debate in the U.S. on the need to maintain legal barriers (firewalls) between commercial and non-traditional banking. However, no theoretical model has yet been developed that examines the joint influence of various factors suggested, such as competition, production economies and regulatory subsidies that affect the bank's incentive to undertake non-traditional activities. This paper applies a stochastic control model to examine the joint effects of these factors on a bank's optimal investment decisions in non-traditional banking and develops some empirically testable hypotheses.