【正文】 。在該文件中表明，只要罰款成本低于最優(yōu)政策那么總是會(huì)低于零，一個(gè)簡(jiǎn)單的數(shù)值計(jì)算方法考慮到四個(gè)重要的數(shù)字。對(duì)貨幣的交易需求應(yīng)該考慮透支現(xiàn)金設(shè)施的可能性。但是由于它技術(shù)上的困難基本上只能取得一般情況下封閉的形勢(shì)的方案。 Chang, 1999。這意味著，最低的障礙是零，同時(shí)他們也給了一個(gè)簡(jiǎn)單的數(shù)學(xué)計(jì)算程序用來(lái)計(jì)算其余三個(gè)障礙。假設(shè)線性持有 /懲罰成本，再 加上固定比例的成本控制和現(xiàn)金股票是由廣義布朗運(yùn)動(dòng)描述的動(dòng)態(tài)， Constantinides 和 Richard (1978)首次指出一個(gè)簡(jiǎn)單的最優(yōu)脈沖帶型政策的存在。從對(duì)鮑莫爾，托賓，米勒和奧爾的工作中可以得出，它起源于主要的數(shù)學(xué)模型所使用的理論的交易和預(yù)防性貨幣需求。如果我們?cè)谟邢迺r(shí)間范圍內(nèi)考慮同一個(gè)模型，可以得到一個(gè)進(jìn)步問(wèn)題，同時(shí)我們必須要研究和尋找變分不等式的解決。更多的人像利用 OFA 的一般過(guò)程描述動(dòng) 態(tài)力學(xué)和跳躍擴(kuò)散過(guò)程。雖然我們已經(jīng)解決一些二維例子的問(wèn)題，而且計(jì)算方法適用于更大的尺度，但是當(dāng)然需要越來(lái)越多的計(jì)算成本。利用 Bensoussan and Lions 的功能分析技術(shù)，我們已經(jīng)發(fā)現(xiàn)，始終存在對(duì)于我們現(xiàn)金管理系統(tǒng)的多維最優(yōu)策略。此外，該現(xiàn)貨庫(kù)存動(dòng)態(tài) 可能是相關(guān)的，他們可以在依賴系統(tǒng)的狀態(tài)下漂移和擴(kuò)散。 導(dǎo)言 在本文中，我們提出了一個(gè)通用的方法用來(lái)解決多層面的現(xiàn)金管理問(wèn)題。我們還計(jì)算了在兩線性尺寸和距離成本函數(shù)模型的解，顯示了在這兩個(gè)簡(jiǎn)單的情況下，最優(yōu)政策的表現(xiàn)形態(tài)形狀。在一般假設(shè)情況下，我們認(rèn)為作為 一個(gè)弱解 OFA 的準(zhǔn)變分不等式的加權(quán) 索伯列夫 空間的價(jià)值功能與我們展示的最優(yōu)策略是一個(gè)很大的特點(diǎn)。 BarIlan et al., 2020), but it is basically due to technical difficulties in obtaining closedform solutions for the more general case. However it is an essential feature of liquidity management to allow a negative cash balance (at some penalty rate) and as pointed out in BarIlan (1990), the transaction demand for money should have to consider the possibility of overdraft cash facilities. In Baccarin (2020) the existence results of Constantinides and Richard(1978) are extended to the case of holdingpenalty costs which have also a quadratic term .In that paper it is shown that as long as the penalty costs are ?nite the lowest barrier of the optimal policy is always below zero and a simple numerical algorithm is given to pute the four critical numbers. In a recent paper, BarIlane al.(2020) model the changes in the money stock by a superposition of a Brownian motion and a pound Poisson process Assuming the optimality of a control band policy they derive the relevant discounted costs as function of the barriers by using renewal and martingale techniques. This can allow to approximate the optimal control parameters numerically. Conclusions In this paper we have presented a general method to solve a multidimensional cash management problem. Our solution allows the transaction costs and the holding/penalty costs to be nonlinear functions. Furthermore the cash stocks dynamics may be correlated and they may have drift and diffusion coef?cients which can depend upon the state of the system. These general assumptions are very important to deal with realistic applications. Using the functional analysis techniques of Bensoussan and Lions we have shown that there always exists an optimal policy for our multidimensional cash management system. Moreover ,in order to pute the solution, we have proved the convergence of a numerical scheme which has a strong foundation in the theory of quasivariational inequalities and impulse control. Although we have solved the problem in some twodimensional examples the algorithm remains the same for greater dimensions, requiring, of course, a growing putational cost. There are several directions in which our variational approach can be further investigated .One can think ofa more general process describing the state dynamics, a jumpdiffusion process, and the set of controls could be generalized considering also a continuous control of the drift or introducing temporal lags in implementing the decisions. If we consider the same model with a ?nite time horizon we obtain an evolutionary problem where we have to study and interpret the solutions of aparabolic quasivariational inequality. Ⅲ 8 多層面現(xiàn)金管理系統(tǒng)的最優(yōu)脈沖控制與廣義費(fèi)用函數(shù) (節(jié)選 ) 作者 ： Stefano Baccarin 國(guó)籍： I10122