不确定竞争市场的R&D投资决策分析

本文针对不确定的竞争市场 ,分析降低成本的不可逆 R& D投资决策 .考虑到 R& D结果不确定 ,而这种不确定与投资量有关 ,在利用博弈论方法分析和给出了投资结果不确定的投资期权价值后 ,设随机市场需求规模服从均匀分布 ,本文分析了各种因素对 R& D投资的影响 ,发现较大的市场需求预期和较强的成本节约效果鼓励了 R& D投资 ;相反地 ,较大的成功 R& D所需的最大投资量挫败了 R& D投资 ;而投资期望净收益与投资成本之间的权衡使得存在事前最优投资量最大化投资期权价值     

研究与开发投资的多阶段实物期权分析

本文结合技术不确定性和现金流不确定性及专利保护 ,将 R& D项目划分为 R& D阶段和新产品商业化阶段 ,运用实物期权法 ,对 R& D项目进行分析 .由动态规划方法推倒出有关项目价值评估和投资期权评价的方程式 ,并作相应典型数值分析 .     

一类投资价值为变量的研究与开发项目的Nash解问题

本文考虑一类完全信息下研究与开发 (R& D)项目中的纯策略问题 .设有一个 R& D项目 ,两位风险中性的投资人竞争 .项目需要的投资量至少是 I,投资较多的一方取胜 .项目成功后的价值是确定的 ,但是其价值大小对这两位投资人不一样 (品牌知名度 ,管理水平 ,营销能力等方面的差异导致的价格和销量不同 ) ,我们使用博弈论方法对此进行研究 ,得到的结果显示 :如果他们所实现的项目价值是常量 ,则不存在均衡解 ;而当项目价值是一个关于投资总量的单增函数时 ,则在两位投资人的价值函数的差异较大时 ,存在一个同时还是社会占优的 Nash均衡解 ,在两位投资人的价值函数差异不太大时 ,不存在均衡解 ,此时的竞争会导致社会效益下降 .从而提示政府应当通过一定的方式 (如招投标法 ,审批法 )对投资活动予以控制 .     

石油勘探项目分阶段投资的最优时机选择

针对一次性投资决策理论与方法在石油勘探项目分阶段投资决策中应用的局限性,运用实物期权中的序列投资决策理论与方法,假设勘探储量转让价格服从跳跃扩散过程,构建了石油勘探项目分阶段投资的最优时机选择模型,逆序求解得出各阶段最优投资时机临界值的解析表达式,在此基础上通过案例演算对比分析了一次性投资和分阶段投资的最优时机决策规则.研究结果表明:一次性投资下的最优时机临界值高于分阶段投资下的最优时机临界值,且各阶段的最优投资时机临界值随勘探进程的不断深入呈现逐渐下降的趋势.     

基于中国公司对东道国的R&D投资模式选择

通过建立一组数学模型,用来分析中国公司在发展中国家的R&D投资模式选择,剖析公司对外投资优势和东道国区位优势,运用模型分析法对指标体系进行经济评价,为中国公司对外投资应用提供依据.     

PPP项目中政府补偿与社会资本投资运营决策研究

从社会资本的视角出发研究了政府部门补偿额度的大小对PPP项目中社会资本投资决策和运营决策的影响,通过将政府部门的补偿分为不同的等级,并结合实物期权理论建立模型求解出了不同等级下社会资本投资的临界值和退出的临界值。算例分析表明在考虑政府补偿的情形下,项目经营阶段社会资本退出的临界值远低于其经营成本,项目投资阶段社会资本投资的临界值严格大于其退出的临界值,并且随着政府补偿额度的增加,投资和退出的临界值严格递减。     

含不动产项目的保险公司再保险-投资策略

站在保险公司管理者的角度, 考虑存在不动产项目投资机会时保险公司的再保险--投资策略问题. 假定保险公司可以投资于不动产项目、风险证券和无风险证券, 并通过比例再保险控制风险, 目标是最小化保险公司破产概率并求得相应最佳策略, 包括: 不动产项目投资时机、 再保险比例以及投资于风险证券的金额. 运用混合随机控制-最优停时方法, 得到最优值函数及最佳策略的显式解. 结果表明, 当且仅当其盈余资金多于某一水平(称为投资阈值)时保险公司投资于不动产项目. 进一步的数值算例分析表明: (a)~不动产项目投资的阈值主要受项目收益率影响而与投资金额无明显关系, 收益率越高则投资阈值越低; (b)~市场环境较好(牛市)时项目的投资阈值降低; 反之, 当市场环境较差(熊市)时投资阈值提高.     

基于面板数据模型的研发投入影响因素区域异质性研究——基于医药制造业样本的实证分析

基于面板数据模型研究了新产品经济产出、税收优惠、人力资本等因素对我国东中西部地区医药制造业研发资金投入强度影响.研究发现:1)东中西部地区在R&D投入影响因素上存在差异,其中人力资本、企业内部研发资金投入、税收优惠因素对东部地区R&D投入的显著作用依次增强;2)政府研发资金投入、人力资本、税收优惠、盈利能力对中部地区R&D投入的显著作用依次增强,而新产品经济产出呈现负向作用;3)企业内部研发资金投入对西部地区R&D投入显著作用强于人力资本因素,企业规模、税收优惠呈现出负向作用.建议我国应因地制宜采取相应对策,有效提高东中西部地区医药制造业R&D研发投入,进一步促进我国医药制造业创新能力和水平.     

带停时的奇异型随机控制问题在金融投资模型中的应用

以随机分析的知识和最优控制理论为基础,讨论了一类带停时的奇异型随机控制的折扣费用问题在金融投资模型中的应用,将该带停时的奇异型随机控制模型的受控状态过程和费用函数结构都推广到了最一般的形式,使该模型的应用范围更加广泛.通过讨论一组相应的变分不等式的解,分别对退化和非退化两种情况给出了此随机控制问题的最优策略,相应得出了投资模型中的最佳决策,并且证明了变分不等式的解即为最优费用函数.与以往不同的是,所得的相关结论应用到了金融投资模型中,从而解决了一类金融投资问题.     

保险公司实业项目投资策略研究

考虑保险公司实业项目投资问题. 假定1)保险公司可以选择在某一时刻投资一实业项目(Real investment), 该项投资可以为保险公司带来稳定的资金收入而不影响其风险;2)保险公司可以将盈余资金投资于证券市场, 该市场包含一风险资产.目标是通过最小化破产概率来确定保险公司实业项目投资时间和风险资产的投资金额.运用混合随机控制-最优停时方法,得到值函数的半显式解, 进而得到保险公司的最佳投资策略: 以固定金额投资证券市场; 当保险公司盈余高于一定额度(称为投资门槛)时进行项目投资, 并降低风险资产投资金额.最后采用数值算例分析了不同市场环境下投资门槛与投资金额, 投资收益率之间的关系. 结果表明:1)项目投资所需金额越少、收益率越高, 则项目投资的门槛越低;2)市场环境较好时(牛市)项目的投资门槛提高, 保险公司应较多的投资于证券市场; 反之, 当市场环境较差时(熊市)投资门槛降低,保险公司倾向于实业项目投资.     

Optimal stopping time on discounted semi-Markov processes

This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end.     

An entry-exit model involving construction and abandonment periods

We analyze, using the optimal stopping theory, the entry-exit decision on a project, which takes time to be constructed and abandoned. We obtain the closed-form expressions of optimal start time of entry, optimal start time of exit, and the maximal expected present value of the project. In addition, we examine the effects of construction and abandonment periods on the optimal start times of entry and exit.     

一类投资时点问题的最优停止模型及其等待时间

针对收益流与一次性投入沉淀成本均不确定的一类风险项目,为使其预期总的贴现净收益最大,提出了寻找项目最优投资时点的最优停止模型.这种方法不依赖于金融市场的完备性及市场无套利.借助于高切原理,通过求解一个自由边界问题,得到模型的候选解.运用最优停止理论证明了其的确为最优解,从而显式地给出了该类风险项目的最优投资时点.进一步,显式给出了到达最优时点的平均等待时间.     

重复造林情况下最优伐木时间的经济决策模型

本文根据林木生长的特点及投资理论 ,建立了重复造林条件情况下最优伐木时间的经济决策模型 ,模型分析表明 ,一期造林情况下最优伐木时间迟于无限期重复造林情况下最优伐木时间     

A model for decision problems with continuous time parameter

The concept of statistical decision theory concerning sequential observations is generalized to decision problems, which are based upon a continuous stochastic process.

In this model decision functions are introduced, consisting of a stopping time and a terminal decision rule. A method of discretization shows the connections between the discrete sequential and the continuous model. Concerning Bayes problems we find, that under certain assumptions the decision problem can be viewed as an optimal stopping problem with continuous time parameter.     

Optimal models with maximizing probability of first achieving target value in the preceding stages

Decision makers often face the need of performance guarantee with some sufficiently high probability. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probability criterion for the first achieving target value. The objective is to find a policy that maximizes the probability of the total discounted reward exceeding a target value in the preceding stages. We show that our formulation cannot be described by former models with standard criteria. We provide the properties of the objective functions, optimal value functions and optimal policies. An algorithm for computing the optimal policies for the finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deterministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis, we approximate general models and prove the existence of e-optimal policy for finite state space. We give an example for the reliability of the satellite sy     

The impact of delaying an investment decision on R&D projects in real option game

In a research and development (R&D) investment, the cost and the project value of such an investment are usually uncertain, which thus increases its complexity. Correspondingly, the NPV (Net Present Value) rule fails to evaluate the value of this project exactly, because this method does not take into account the market uncertainty, irreversibility of investment and ability of delay entry. In this paper, we employ the real option theory to evaluate the project value of a R&D investment. Since the cost of a R&D investment is very high and the flow of the information is crowded, an investor cannot make an immediate decision every time. So, the proposed real option model is an exchange option. At the same time, combining the real option and the game theory, we can find the Nash equilibrium which is the optimal strategy. Moreover, we also study how the delayed time influences the price of the project investment and how the different delayed times effect the choice of the optimal strategies.     

The Convergence Rate from Discrete to Continuous Optimal Investment Stopping Problem

The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al. (2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations (BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.     

Consumption-Investment Problem with Subsistence Consumption,Bankruptcy, and Random Market Coefficients

We consider a general continuous-time finite-horizon single-agent consumption and portfolio decision problem with subsistence consumption and value of bankruptcy. Our analysis allows for random market coefficients and general continuously differentiable concave utility functions. We study the time of bankruptcy as a problem of optimal stopping, and succeed in obtaining explicit formulas for the optimal consumption and wealth processes in terms of the optimal bankruptcy time. This paper extends the results of Karatzas, Lehoczky, and Shreve (Ref. 1) on the maximization of expected utility from consumption in a financial market with random coefficients by incorporating subsistence consumption and bankruptcy. It also addresses the random coefficients and finite-horizon version of the problem treated by Sethi, Taksar, and Presman (Ref. 2). The mathematical tools used in our analysis are optimal stopping, stochastic control, martingale theory, and Girsanov change of measure.