Explicit formula for the optimal government debt ceiling

Motivated by the current debt crisis in the world, we develop a stochastic debt control model to study the optimal government debt ceiling, or equivalently the optimal ceiling for government debt. We consider a government that wants to control its debt by imposing an upper bound or ceiling on its debt-to-GDP ratio. We assume that debt generates a cost for the country, and this cost is an increasing and convex function of debt ratio. The government can intervene to reduce its debt ratio, but there is a cost generated by this reduction. The goal of the government is to find the optimal control that minimizes the expected total cost. We obtain an explicit solution for the government debt problem, that gives an explicit formula for optimal government debt ceiling. Moreover, we derive a rule for optimal debt policy in terms of the optimal government debt ceiling. In an extension of the model, we find that countries with a strong positive link between debt and economic growth should have a high optimal debt ceiling. This paper provides the first theoretical model for the optimal government debt ceiling.     

Government Debt, Budget Surplus, and Popularity of Politicians

This paper sets up a positive model of government behavior to determine the optimal fiscal policy of a politician who aims to reach a certain target level of national debt and remain popular at the same time. We model explicitly the response of the citizens to the fiscal policy set by the politician. To that end, we assume that citizens form an equilibrium acceptance rate of savings and adjust dynamically this savings rate to the currently prevailing levels of government debt and primary surplus. The difference between the equilibrium acceptance rate of savings as formed by the public and the fiscal policy actually chosen by the politician determines the politician popularity. Using the Pontryagin maximum principle, we derive the optimal level of the fiscal policy and investigate its local stability depending on the parameters of the model. We show that cyclical strategies [that is, phases of saving (primary surplus) and spending (primary deficit)], may be optimal.     

Regional multiple objective quantitative economic policy: a Belgian model

Already thirty years ago, L.R. Klein [10], R. Frisch [5], J. Tinbergen [16] and H. Theil [13] introduced the subject of quantitative economic policy. More recently, multiple objective decision making has been suggested for the quantitative determination of macro-economic policy.In this paper we present an application of multiple criteria interactive linear programming for policy analysis on the regional level. The multiregional economic model considered distinguishes the nine Belgian provinces and emphasizes on the interrelations between them.     

Pricing non-storable perishable goods by using a purchase restriction: General optimality results

The aim of this paper is to investigate the validity of the optimality results derived from [Eur. J. Oper. Res. 134 (2001) 631] by relaxing the following two assumptions: (a) the firm offers restricted units first and then unrestricted units later at higher price levels, and (b) only one type of product is available during the whole selling process. In the absence of (a), we establish a general optimality theorem, which shows that any optimal policy in [Eur. J. Oper. Res. 134 (2001) 631] remains to be optimal in the class of general policies that allow the restriction to be attached at any price level. For the simultaneous availability issue associated with (b), we demonstrate that there always exists an optimal policy that is sustainable even when all active prices are made available at the same time. These two results assure the relevance of the theoretical model in [Eur. J. Oper. Res. 134 (2001) 631] to current yield management practices and further improve our understanding on the role and the impact of a well-designed purchase restriction on pricing decisions.     

Dynamic Control and Optimization of Capital-Constrained Stochastic Inventory Systems

For most firms,especially the small-and medium-sized ones,the operational decisions are affected by their internal capital and ability to obtain external capital.However,the majority of the current studies on dynamic inventory control ignore the firm’s financial status and financing issues completely.An important question that arises is:what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital?In this paper,we review some of the latest developments in this area.After a brief review of single period models,we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth.Two cases are discussed in detail:self-finance and short term finance.In the first case,the firm has to rely on its own capital for all ordering decisions,while in the second,the firm can borrow short term loan from lenders.A detailed characterization of the optimal policy is presented and its managerial insights are discussed.Several possible extensions are suggested.     

坏账和延期支付策略下采购商最优订货模型

在供应商、采购商及其顾客组成的三级供应链结构中,供应商提供给采购商较长的延期支付期限,采购商提供给其顾客较短的延期支付期限。且由于顾客为不特定多数,存在一定的坏账风险。文章从采购商的角度出发,分析在二阶延期支付策略下,坏账影响下采购商的最优订货策略。首先,考虑到坏账会影响采购商的利息收入和利息支出,因此文章从低坏账率和高坏账率两种情形出发,探讨了坏账影响下采购商的利息收入与利息支出,建立了相应的决策模型。其次,通过模型的分析求解,得出采购商的最优订货周期和最优订货批量的判定方法,进一步分析了各参数对采购商最优决策的影响。最后,通过数值分析对有关结论进行了验证,文章的分析研究不仅具有一定的理论意义,而且可以更好地指导采购商的订货决策。     

Optimal purchasing policy in a two-component assembly system with different purchasing contracts for each component

This paper considers an assembly system where a firm produces a single product which is assembled using two types of components (component 1 and component 2). The components are provided by individual suppliers (supplier 1 and supplier 2). We assume that the firm makes different procurement contracts with supplier 1 and supplier 2. To supplier 1, the firm specifies the maximum inventory level of component 1 and makes a commitment to purchase the component as long as its inventory level is below this target level. To supplier 2, the firm has the option of purchasing or rejecting component 2 at each instant supplier 2 provides it. Formulating our model as a Markov decision problem, we identify a component 2 purchasing policy which maximizes the firm’s profits subject to the costs of rejecting component 1, holding component 2, and purchasing component 2. We also investigate how the changes in the sales price and cost parameters affect the optimal purchasing policy. Finally, we present numerical study for the optimal performance evaluation.This material is based upon work supported by the Korea Science and Engineering Foundation (KOSEF) through the Northeast Asia e-Logistics Research Center at University of Incheon.     

基于减排框架的最优技术政策选择研究

基于减排框架,本文分别引入研发补贴政策、研发卡特尔(简称“R&D卡特尔”)、竞争研发联盟(简称“RJV竞争”)及卡特尔研发联盟(简称“RJV卡特尔”)等四种技术政策,构建了一个多阶段博弈模型,研究单一技术政策、技术组合政策情形下双寡头企业减排研发绩效、利润及社会福利水平,并进一步利用数值模拟方法探讨政府和企业最优的技术政策选择,政府和企业最优技术政策选择结果的差异及其影响因素。研究结论表明:首先,从政府角度来看,组合政策的效果总是相对优于单一技术政策,并且政府最优的技术政策选择为RJV卡特尔与补贴组合政策。其次,无论溢出率取何值,政府和企业最优的技术政策选择都是一致的。最后,排污税取值影响政府和企业最优技术选择的一致性,当排污税较小时,企业最优的技术政策选择为RJV竞争与补贴组合政策(或RJV竞争政策);当排污税较大时,企业最优的技术选择为单一的技术政策。为了使政府和企业的最优技术政策选择一致,政府应选择一个合适的排污税。     

动态环境约束下企业的资本积累

本文讨论动态环境约束下企业的动态投资行为,拓广了文献[4]的结果.为了使讨论的问题更符合实际情况,本文假设政府设定的污染排放上限是与企业的规模大小有关,即假设污染排放上限是生产资本的函数,讨论动态环境约束下企业的最佳动态投资行为,并为政府制定污染排放政策提供依据.     

Stocking and pricing decisions under endogenous demand and reference point effects

In this paper, we study the newsvendor’s pricing and stocking decisions under reference point effects. The demand faced by the newsvendor is endogenous and the customers may also decide to procure the product from an outside option. We characterize the firm’s optimal pricing and stocking decisions. Our analysis reveals a threshold policy on the firm’s ordering and pricing decisions while considering the impact of reference point effects. We also find that as the level of optimism increases, the firm’s optimal ordering level decreases and optimal price increases. We further study the impact of loss aversion on the firm’s ordering and pricing decisions.     

Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand

In this paper, we discuss how a capital-constrained retailer determines his optimal advertising/ordering policy and selects his financing mode when he faces the following modes: no financing service, bank financing, and supplier/mixed financing. For each mode, we construct an optimization model and present a method for how the retailer determines his corresponding optimal advertising and ordering policies in the terms of his initial capital level. Furthermore, we derive the conditions of retailer selecting the optimal financing mode based on both his initial capital level and the interest rates of the financing services. We show that when the retailer is relatively “poor,” he prefers bank financing mode if the bank interest rate is lower than the supplier, otherwise mixed financing mode; when he is moderately “rich,” he only selects supplier financing mode if the bank interest rate is greater than a threshold value and otherwise bank financing mode; however, when he is relatively “rich,” he always chooses bank financing mode even if the bank interest rate is higher than the supplier. We conduct numerical studies to illustrate the theoretical results and find adopting financing service significantly improves the retailer’s performance especially when he has relatively low initial capital level.     

Valuation of life insurance products under stochastic interest rates

In this paper, we introduce a consistent pricing method for life insurance products whose benefits are contingent on the level of interest rates. Since these products involve mortality as well as financial risks, we present an approach that introduces stochastic models for insurance products through stochastic interest rate models. Similar to Black et al. [Black, Fisher, Derman, Emanuel, Toy, William, 1990. A one-factor model of interest rates and its application to treasury bond options. Financ. Anal. J. 46 (January-February), 33-39], we assume that the premiums and volatilities of standard insurance products are given exogenously. We then project insurance prices to extract underlying martingale probability structures. Numerical examples on variable annuities are provided to illustrate the implementation of this method.     

An optimal regulation of a storage level with application to the water level regulation of a lake

In [10] a system of stochastic programming models was introduced for the optimal control of a storage level. Each model in this system serves to determine the optimal policy for only one period ahead though the time horizon consists of many future periods. The optimal control thus obtained can be considered an open loop control methodology. The main purpose of this paper is to present an application by giving an optimal control method for the regulation of the water level of Lake Balaton in Hungary. By solving almost 600 stochastic programming problems we analyze what would have happened if we had controlled the water level using our method between 1922 and 1970, where one decision period is one month. The numerical results show that the proposed control methodology works quite well in this case.     

债务期限和资本结构的联合影响因素:一个结构方程模型

在考虑债务期限与资本结构相互依赖关系下,通过构建结构方程模型,采用中国上市公司面板数据,应用2SLS对债务期限和资本结构的联合影响因素进行经验检查,以拓展先前研究。研究发现,债务期限与资本结构是联立决定的,债务水平高的公司具有更多的长期债务,同时,长期债务多的公司具有更高的债务水平。     

带干扰的常利率超额再保险Poisson风险模型的最优自留额

本文推广了Centeno[1],何树红[2],张茂军[3]的模型,研究带干扰的常利率超额再保险风险模型。首先用鞅方法求得其调节函数,进而证明Lundberg不等式,给出有限时间破产概率上界,并讨论最优自留额的确定。     

Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants

We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firm's asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firm's total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firm's assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model.     

Optimal dividends and bankruptcy procedures: Analysis of the Ornstein-Uhlenbeck process

This paper investigates the impact of bankruptcy procedures on optimal dividend barrier policies. We specifically focus on Chapter 11 of the US Bankruptcy Code, which allows a firm in default to continue its business for a certain period of time. Our model is based on the surplus of a firm that earns investment income at a constant rate of credit interest when it is in a creditworthy condition. The firm pays a debit interest rate that depends on the deficit level when it is in financial distress. Thus, the surplus follows an Ornstein-Uhlenbeck (OU) process with a negative surplus-dependent mean-reverting rate. Default and liquidation are modeled as distinguishable events by using an excursion time or occupation time framework. This paper demonstrates how the optimal dividend barrier can be obtained by deriving a closed-form solution for the dividend value function. It also characterizes the distributional property and expectation of bankruptcy time subject to the bankruptcy procedure. Our numerical examples show that under an optimal dividend barrier strategy, the bankruptcy procedure may not prolong the expected bankruptcy time in some situations.     

A projection method for phase field models in micromagnetics

Magnetic materials have been finding increasingly wider areas of application in industry and therefore, as indicated by the reviews [1], [2] and [3], there is an increased interest in the efficient modeling of such materials that have an inherent coupling between the magnetic and mechanical characteristics. A particular challenge in the modeling of such materials is the algorithmic preservation of the geometric constraint on the magnetization field, that remains constant in magnitude [4]. In earlier works, [5] and [6], we presented a phase field model within a geometrically exact incremental variational framework where the geometric property of the magnetization director is exactly preserved pointwise by nonlinear rotational updates at the nodes. In the current work however, we present an alternative approach that involves an operator split along with a projection step for the magnetization vector. This method provides significant advantages in terms of speed and ease of implementation at the cost of the maximum time step size used. The current work therefore presents comparative study of the the two methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal dividends and bankruptcy procedures: Analysis of the Ornstein–Uhlenbeck process

This paper investigates the impact of bankruptcy procedures on optimal dividend barrier policies. We specifically focus on Chapter 11 of the US Bankruptcy Code, which allows a firm in default to continue its business for a certain period of time. Our model is based on the surplus of a firm that earns investment income at a constant rate of credit interest when it is in a creditworthy condition. The firm pays a debit interest rate that depends on the deficit level when it is in financial distress. Thus, the surplus follows an Ornstein–Uhlenbeck (OU) process with a negative surplus-dependent mean-reverting rate. Default and liquidation are modeled as distinguishable events by using an excursion time or occupation time framework. This paper demonstrates how the optimal dividend barrier can be obtained by deriving a closed-form solution for the dividend value function. It also characterizes the distributional property and expectation of bankruptcy time subject to the bankruptcy procedure. Our numerical examples show that under an optimal dividend barrier strategy, the bankruptcy procedure may not prolong the expected bankruptcy time in some situations.     

Irreversible capital accumulation under interest rate uncertainty

We consider the optimal sequential irreversible investment policy of a value maximizing firm facing decreasing returns to scale and interest rate uncertainty. We characterize the optimal accumulation policy and its value for a broad class of diffusion models of the short interest rate by focusing on the marginal investment decision and deriving the marginal value of capital explicitly. We also state a set of conditions under which there is a maximal capital stock above which the option to expand productive capacity further in the future becomes valueless. Hence, our results indicate that interest rate uncertainty may limit the size of an optimally investing firm.