Optimal impulse control for cash management¶with quadratic holding-penalty costs

Abstract

This paper studies optimal control for an infinite horizon cash management problem where the cash fund fluctuates as a Brownian motion. Holding-penalty costs are assumed to be a quadratic function of the cash level and there are fixed and proportional transaction costs. Using the "impulse technique", we prove that optimal control exists and takes the form of a control band policy. (2000): 93E20, 49K45 Mathematics Subject Classification

Data-Driven Decision-Making and Its Application to the Corporate Cash Management Problem

“…Cost functions. The linear cost assumption is also a common pattern with the exception of Baccarin (2002) and Baccarin (2009), that considered quadratic holding and penalty costs. However, there also exist differences in the linear approach.…”

“…This model was later extended to the case of quadratic holding-penalty costs in Baccarin (2002), and to a multidimensional cash management system and general cost functions in Baccarin (2009), when cash balances fluctuates as a diffusion process. Premachandra (2004) also used a diffusion process to propose a more generalized version of the Miller-Orr model which relaxes most of its restrictive assumptions.…”

“…Furthermore, it represents the origin of a number of recent works (Baccarin, 2002;Premachandra, 2004;Baccarin, 2009) on cash management. However, the strong assumption on modeling cash flows as a diffusion process represents a serious limitation in practical applications.…”

“…To the best of our knowledge, quadratic holding and penalty costs where considered for the first time in Baccarin (2002). Furthermore, a general multidimensional approach to the cash management problem was also first introduced by Baccarin (2009) using generalized cost functions and providing theoretical results for two bank accounts.…”

“…In addition, Baccarin (2002) and Baccarin (2009) considered the case of cash balance fluctuations following a diffusion process. Smith (1986) and Premachandra (2004) also used a diffusion process to propose generalized versions of the Baumol-Tobin model (Frenkel and Jovanovic, 1980), and the Miller and Orr (1966) model, respectively.…”