Optimal cash management under uncertainty

Abstract

The problem of optimal investment in two types of assets over time is formulated as a stochastic optimal control problem. The two assets considered are a bank account and stock. The earnings derived from stock consist of dividends and capital gains. The randomness in the return on stock is modeled using a standard Brownian motion. Using a stochastic maximum principle, an explicit decision rule of the bang-bang type is derived for optimal management of cash.

Target indicators of the company’s asset management in a volatile economy

“…Шерман [6], А. Бенсусан, А. Чутани, С.П. Сетхи [7], Дж. Энквист, М. Грэхэм, Ю. Никкинс [8], Вьет Ань Данг, Мин Чжу Ким, Юнчеол Шин [9], Б. Эппухэми [10].…”

On Optimal Cash Management under a Stochastic Volatility Model

“…We consider an optimal cash management problem, by extending the model in Ref. [1]. We assume that the firm invests its cash in a bank account and a stock in a portfolio of value w(t) at time t, and the proportion of wealth invested in the stock attime t is u(t).…”

“…Sethi and Thompson [10] presented a deterministic model allowing for time-varying cash demand, and solved the cash management problem using maximum principles in both discrete-time and continuous-time frameworks. Bensoussan et al [1] extended the Sethi-Thompson model to allow capital gains on stock, and also presented a stochastic model where the rate of growth in the price of the stock is considered random. Using the stochastic maximum principle, they obtained an analytic solution for the optimal cash management problem.…”

“…In the stochastic model developed by Bensoussan et al [1], the volatility of the stock dividends is a deterministic function of time, and we introduce a Stochastic Volatility (SV) model for the rate of growth in the price of a stock. In stochastic volatility models, the volatility changes randomly over time according to some stochastic differential equations or some discrete-time random processes, which have been widely used in financial economics and mathematical finance.…”

The optimal cash holding models for stochastic cash management of continuous time

“…In the Miller and Orr's model, it is moreover highlighted that the cash balance follows a normal distribution, which may be a very ideal state. Since then, a few scholars, including Girgis (1968) [16], Eppen and Fama (1969) [12], Daellenbach (1971Daellenbach ( , 1974 [9] [10], Hausman and Sanchez-Bell (1975) [17], Milbourne (1983) [22], Vickson (1985) [29] and Smith (1989) [26], Baccarin (2002) [1] and Bensoussan, Chutani and Sethi(2009) [7], have tried to overcome the defects by using dynamic programming methods. See also Song, Ching, Siu and Yiu (2013) [27] for a recent discussion on the issue.…”