Optimal tax depreciation with uncertain future cash-flows

Since taxable income consists of cash-flows reduced with depreciation charges, the choice of the depreciation method affects taxable income in future periods. A manager can therefore try to minimize the present value of future tax payments by choosing a particular depreciation method among those that are accepted by the tax authorities. We focus here on the choice between the two most commonly used methods in practice, i.e. the straight line depreciation method (SDM) and an accelerated depreciation method (ADM), such as the double declining balance (DDB) method and the sum of the years–digits (SYD) method. We show how the optimal choice depends on the discount factor, the degree of uncertainty in future cash-flows, and the structure of the tax system.     

Stationary dual prices and depreciation

This paper models a machine replacement and capacity expansion problem as an infinite-horizon linear program. We establish a strong duality result and show that stationary dual prices are optimal, regardless of initial conditions. These prices measure the economic value of owning vintage machinery and thus define depreciation schedules. We present necessary and sufficient conditions for straight-line depreciation.This work was partially supported by grants ECS-8312008 and ECS-8619732 from the National Science Foundation.     

The effect of tax depreciation on the stochastic replacement policy

The optimal replacement policy for an asset subject to a stochastic deteriorating operating cost is determined for three different tax depreciation schedules and a known re-investment cost, as the solution to a two-factor model using a quasi-analytical method. We find that tax depreciation exerts a critical influence over the replacement policy by lowering the operating cost thresholds. Although typically a decline in the corporate tax rate, increase in any initial capital allowance, or decrease in the depreciation lifetime (increase in depreciation rate) results in a lower operating cost threshold which justifies replacing older equipment, these results are not universal, and indeed for younger age assets the result may be the opposite. An accelerating depreciation schedule may incentivize early replacement in a deterministic context, but not necessarily for an environment of uncertainty.     

Depreciation games

The main aim of this paper is to show how Game Theory can be used in the day-to-day running of a company. No precedent, as far as we know, in the literature of the application of Cooperative Game Theory in order to obtain new depreciation methods for a fixed asset which is owned by a company. To this end, we will first illustrate the usual depreciation methods employed in accountancy. Then, with the objective of finding new depreciation methods, we will establish the relationship between Game Theory and Accountancy. On the basis of this relationship we introduce some new depreciation methods. Finally, a family of solutions is defined which improves the properties of traditional and previously introduced methods. Financial support from the Generalitat Valenciana through project GV05/077 is gratefully acknowledged by J. Aparicio. Financial support from the Generalitat Valenciana through project GRUPOS04/79 and from the Ministerio de Educación y Ciencia through project HI2002/0032 are gratefully acknowledged by J. Sánchez-Soriano.     

Optimal design of personalized prostate cancer therapy using Infinitesimal Perturbation Analysis

The standard treatment for advanced prostate cancer is hormone therapy in the form of continuous androgen suppression (CAS), which unfortunately frequently leads to resistance and relapse. An alternative scheme is intermittent androgen suppression (IAS), in which patients are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. In spite of extensive recent clinical experience with IAS, the design of ideal protocols for any given patient remains a challenge. The level of prostate specific antigen (PSA) is frequently monitored to determine when patients will be taken off therapy and when therapy will resume. In this work, we propose a threshold-based policy for optimal IAS therapy design that is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under IAS and perform Infinitesimal Perturbation Analysis (IPA) to adaptively adjust PSA threshold values so as to improve therapy outcomes. We also apply this methodology to clinical data from real patients, and obtain promising results and valuable insights for personalized IAS therapy design.     

Risk management strategies via minimax portfolio optimization

Recent extreme economic developments nearing a worst-case scenario motivate further examination of minimax linear programming approaches for portfolio optimization. Risk measured as the worst-case return is employed and a portfolio from maximizing returns subject to a risk threshold is constructed. Minimax model properties are developed and parametric analysis of the risk threshold connects this model to expected value along a continuum, revealing an efficient frontier segmenting investors by risk preference. Divergence of minimax model results from expected value is quantified and a set of possible prior distributions expressing a degree of Knightian uncertainty corresponding to risk preference determined. The minimax model will maximize return with respect to one of these prior distributions providing valuable insight regarding an investor’s risk attitude and decision behavior. Linear programming models for financial firms to assist individual investors to hedge against losses by buying insurance and a model for designing variable annuities are proposed.     

Current-Cost Deepreciation: Estimation and Optimization

In recent years, current-cost accounting (CCA) has receivedconsiderable attention throughout the Western industrializedworld. However, both in the academic and professional literature,the debate over the utility of CCA has been almost exclusivelyconfined to the theoretical level. The practical issue of obtainingreliable and accurate methods for estimating the various CCAadjustments has been almost totally ignored. In this respect,the present note outlines techniques which may be used to estimatecurrent-cost depreciation. Specifically, using standard techniquesfrom the discipline of numerical mathematics, integration formulaeare derived by which current-cost depreciation may be estimated.It is shown that professional accounting bodies have unknowinglyrecommended use of the simplest Newton-Cotes closed integrationformulae and that more precise estimates may be obtained byemploying higher-level Newton-Cotes rules. Alternatively, Gaussianquadrature methods may be employed, though these have the disadvantageof using unevenly spaced nodes or quadrature points. The paperthen derives optimal current-cost depreciation rules for firmswho, for political reasons, desire to minimize reported profits.It is shown that, at a theoretical level at least, this problemis reduced to one in the calculus of variations.     

A dynamic programming model for effect of worker’s type on wage arrears

We analyze how wage arrears are affected by the worker’s type (in this paper, the worker’s type means the worker’s attitude to wage arrears). Wage arrears cause workers’ negative emotion which may lead to serious social problem and the government may intervene. In this paper, we model the process of wage arrears as a Markov decision process in which the firm is the decision maker. We develop an optimal solution approach under the assumption that the worker’s negative emotion threshold (The worker’s negative emotion increases monotonically with increasing back pay. Once the cumulative back pay exceeds a particular value, the worker will take legal actions and the government will intervene. We define the particular value as the worker’s negative emotion threshold.) is normally distributed and provide insights into how wage arrears vary with the worker’s type and the government intervention. We propose the optimal government intervention which stops wage arrears and does not disturb the normal order of the market economy. We show that the intervention depends on the worker’s type and the results imply that the government intervention should be adjusted dynamically according to different regions, industrial sectors and time periods.     

A learning curve model with knowledge depreciation

Empirical studies in several industries have verified that unit costs decline as organizations gain experience or knowledge in production, which is referred to as the learning curve effect. In the past two decades, there has also been analytical work on the relationship between a firm's learning curve effects and its pricing and output decisions. Learning rates differ significantly across firms in the same industry and recent empirical evidence has shown that knowledge depreciation may be an important reason for these differences. We propose and analyze a learning curve model with knowledge depreciation and provide several new insights. First, we show that there exists a steady state where knowledge level and unit cost remain constant over time and there exists an optimal path to this steady state. Many empirical researchers have observed this ‘plateau’ phenomenon, whereby unit costs decline but reach saturation after some time. While this has been traditionally modeled exogenously in the learning curve literature by assuming that cost reduction stops at some level of knowledge through a convex, decreasing unit cost function, we provide an alternative endogenous explanation. We are also able to show that, unlike in the model without knowledge depreciation, the production rate along the optimal path to the steady state may decrease over time. Also, the knowledge level along the optimal path may actually decline over time. Finally, we show that the optimal production rate decreases at higher interest rates and increases at higher knowledge depreciation rates. In turn, this implies that a high interest rate environment discourages firms from achieving high knowledge levels and results in higher prices. On the other hand, higher knowledge depreciation rates result in higher production rates and lower prices.     

Optimal Dynamic Investment Policy for Different Tax Depreciation Rates and Economic Depreciation Rates

This paper analyzes the investment policy consequences of incorporating a tax depreciation rate different from the economic depreciation rate. Most often, firms choose their tax depreciation rate in a strategic way. Therefore, it would be a coincidence, should the optimization process lead to a tax depreciation rate that equals the economic depreciation rate. The implications of a difference between tax depreciation rate and economic depreciation rate are investigated in an optimal control model for the determination of the firm investment policy over time.     

存在破产成本时保理授信下供应商赊销策略研究

在存在破产成本的前提下,构建了保理商确定授信额度的量化模型,并研究了供应商如何在保理授信下确定赊销量的问题。研究结果表明,保理商的授信以保理费率不低于临界值为前提。当保理费率高于一定水平时,授信额度较高,供应商将在额度内进行赊销交易。否则,供应商将超出授信额度进行赊销交易,并且此时,若固定破产成本高于阈值,供应商最优赊销量存在上限,保理对供应链的作用主要体现在其风险分担功能上;若固定破产成本低于阈值,供应商最优赊销量存在下限,保理对供应链的作用主要体现在其融资功能上。     

高阶优化算法分析简介

高阶优化算法是利用目标函数的高阶导数信息进行优化的算法,是最优化领域中的一个新兴的研究方向.高阶算法具有更低的迭代复杂度,但是需要求解一个更难的子问题.主要介绍三种高阶算法,分别为求解凸问题的高阶加速张量算法和A-HPE框架下的最优张量算法,以及求解非凸问题的ARp算法.同时也介绍了怎样求解高阶算法的子问题.希望通过对高阶算法的介绍,引起更多学者的关注与重视.     

一种新的恒加试验下双参数指数型产品的可靠性分析

针对双参数指数型产品,在具有二项移走(即在每个观测时刻产品的移走数服从二项分布)的分组寿命试验下,研究了分组时刻的确定方法,推导出门限参数、寿命参数和移走概率的极大似然估计。进而,讨论了双参数指数型产品在具有二项移走的恒加寿命分组试验下的可靠性分析问题。利用加速寿命方程,给出了双参数指数型产品的可靠性估计。最后给出随机模拟例子验证了结论的正确性。     

Upward straight-line embeddings of directed graphs into point sets

In this paper we study the problem of computing an upward straight-line embedding of a planar DAG (directed acyclic graph) G into a point set S, i.e. a planar drawing of G such that each vertex is mapped to a point of S, each edge is drawn as a straight-line segment, and all the edges are oriented according to a common direction. In particular, we show that no biconnected DAG admits an upward straight-line embedding into every point set in convex position. We provide a characterization of the family of DAGs that admit an upward straight-line embedding into every convex point set such that the points with the largest and the smallest y-coordinate are consecutive in the convex hull of the point set. We characterize the family of DAGs that contain a Hamiltonian directed path and that admit an upward straight-line embedding into every point set in general position. We also prove that a DAG whose underlying graph is a tree does not always have an upward straight-line embedding into a point set in convex position and we describe how to construct such an embedding for a DAG whose underlying graph is a path. Finally, we give results about the embeddability of some sub-classes of DAGs whose underlying graphs are trees on point set in convex and in general position.     

Threshold policies for controlled retrial queues with heterogeneous servers

Retrial queues are an important stochastic model for many telecommunication systems. In order to construct competitive networks it is necessary to investigate ways for optimal control. This paper considers K -server retrial systems with arrivals governed by Neut' Markovian arrival process, and heterogeneous service time distributions of general phase-type. We show that the optimal policy which minimizes the number of customers in the system is of a threshold type with threshold levels depending on the states of the arrival and service processes. An algorithm for the numerical evaluation of an optimal control is proposed on the basis of Howar's iteration algorithm. Finally, some numerical results will be given in order to illustrate the system dynamics. AMS subject classification: 60K25 93E20     

The Chebyshev–Shamanskii Method for Solving Systems of Nonlinear Equations

We present a method, based on the Chebyshev third-order algorithm and accelerated by a Shamanskii-like process, for solving nonlinear systems of equations. We show that this new method has a quintic convergence order. We will also focus on efficiency of high-order methods and more precisely on our new Chebyshev–Shamanskii method. We also identify the optimal use of the same Jacobian in the Shamanskii process applied to the Chebyshev method. Some numerical illustrations will confirm our theoretical analysis.     

A δ-shock maintenance model for a deteriorating system

In this paper, a δ-shock maintenance model for a deteriorating system is studied. Assume that shocks arrive according to a renewal process, the interarrival time of shocks has a Weibull distribution or gamma distribution. Whenever an interarrival time of shocks is less than a threshold, the system fails. Assume further the system is deteriorating so that the successive threshold values are geometrically nondecreasing, and the consecutive repair times after failure form an increasing geometric process. A replacement policy N is adopted by which the system will be replaced by an identical new one at the time following the Nth failure. Then the long-run average cost per unit time is evaluated. Afterwards, an optimal policy N^* for minimizing the long-run average cost per unit time could be determined numerically.     

The effect of depreciation allowances on the timing of investment and government tax revenue

We develop a model of the behavior of a potential investor (under uncertainty and in a fiscal environment) who wishes to invest into a project in the real sector of an economy and faces a timing problem. We find an optimal solution within this model and examine the dependence of the tax revenue from the newly created firm on the depreciation policy. It is shown that there exists a domain in the space of the parameters of the investment project where both the tax revenue and the incentives can be increased by using the depreciation policy.     

不确定需求下页岩气开发项目投资时机与钻井数量选择研究

基于工程化实现视角,结合规划产能与实际产出的不一致性和产量递减性,构建市场需求不确定情境下页岩气开发项目的投资时机与钻井数量决策模型,给出最佳投资时机和最优钻井数量的解析解,并探讨了不确定性、产量递减率、钻井成功率以及钻井成本变动对最佳投资时机和最优钻井数量的影响。结果表明最佳投资时机受单位有效钻井成本影响却与最优钻井数量多少无关,最优钻井数量受市场需求的期望增长率和波动影响而与市场需求量大小无关;不确定性、产量递减率或钻井成本的增大,将引起投资延迟和钻井数量增加,而钻井成功率的增大则会起到相反的作用;并发现投资阈值与最优钻井数量呈同向变动规律。     

两货栈及延期支付和现金折扣情形下变质产品的最优订货策略

已有的两货栈库存模型通常不考虑将延期支付和现金折扣相结合的情形,但实际上,供应商在给予销售商延期支付政策的同时,也会实施现金折扣策略以激励销售商尽快付款,加快资金周转,减少坏账损失。为此,本文建立了延期支付和现金折扣情形下变质产品的两货栈库存模型,并对模型的最优解进行理论分析,给出了最优解的求解步骤。最后通过数值算例对模型的可行性进行了验证,并分析了模型参数变化对最优订货策略和最优付款时间的影响。