非对称情形下R＆D竞争项目的策略性投资

在非对称情形下,考虑具有技术不确定和未来收益不确定的竞争研究与开发(R&D)项目的不可逆策略性投资.利用期权博弈理论和随机优化方法给出了高效研发公司(主导者)的最优投资阈值和最优投资规则的解析表达式,并证明了由于两公司的竞争使投资阈值下降.其次讨论了两公司的混合投资策略,并给出每个公司执行投资期权的概率和两公司同时执行投资期权的概率.在最后给出了数值模拟算例来说明该文结论的合理性.     

非对称情形下R & D竞争项目的策略性投资

在非对称情形下,考虑具有技术不确定和未来收益不确定的竞争研究与开发(R&;D)项目的不可逆策略性投资.利用期权博弈理论和随机优化方法给出了高效研发公司(主导者) 的最优投资阈值和最优投资规则的解析表达式,并证明了由于两公司的竞争使投资阈值下降.其次讨论了两公司的混合投资策略,并给出每个公司执行投资期权的概率和两公司同时执行投资期权的概率. 在最后给出了数值模拟算例来说明该文结论的合理性.     

不确定的时间范围下含期权的最优投资决策

不同于以往研究的含期权的最优投资消费决策,研究了不确定的时间范围下含期权的最优投资决策,运用动态规划原理和随机分析的方法,解决对应的最优控制问题,最优策略可通过对应的HJB方程得到,并显式地得到了HARA效用下的最优投资策略及最优财富过程.     

期权对冲下零售商最优订货策略及供应链协调机制

考虑到市场需求与金融衍生品标的资产之间的关联性,在供应链契约中同时引入看涨期权和看跌期权.首先,在线性相关条件下,得到了基于期权对冲的零售商最优订货策略,结果表明零售商能够利用期权对冲策略获得最大期望收益.其次,进一步基于看涨看跌期权定价理论探索了供应链协调机制,剖析了看涨看跌期权对供应链整体收益的作用,发现利用期权对冲策略可获得供应链最大期望利润.最后,用数值算例分析p,c,m,S₀,r,T,σ对利润及最优订货策略的影响.     

切换成本对线性市场投资决策影响的实物期权分析

本文基于Hotelling模型,针对一个企业在线性区域内的投资决策,考虑投资者在采用为自己作为新进入公司,为新客户使用本公司的产品付出切换成本来竞争市场的策略行为,建立需求不确定环境中的连续动态模型,应用实物期权分析方法评价投资者的投资机会价值和最优投资策略,研究切换成本对投资者投资机会的价值和投资决策的影响.本文研究结果给出了投资者在付出切换成本获得市场份额和减少成本增加投资价值之间的权衡.     

基于CvaR的融入期权的投资组合模型

把期权作为一种投资对象融入到投资组合中,而不仅仅是作为风险对冲工具.用条件风险价值(CVaR)刻画组合风险,并求出最小化风险下的最优鲁棒投资组合策略.最后通过数值算例证明了模型的有效性,并得到融入期权后有效地提高了组合的收益,特别是当标的资产出现大的波动时,期权在组合中的表现更突出.     

双币种博弈期权

博弈期权是一种赋予期权出售方在期权有效期内任意时刻可以赎回合约权利的美式期权.在B-S框架下分析了双币种情形下的博弈期权定价行为,建立了双币种博弈期权的定价模型,分别讨论了敲定价以国内货币计价和国外货币计价下的博弈期权定价问题及其最优赎回策略,通过运用偏微分方程的方法得到了这两种情形下期权价格的表达式及其最优执行边界.最后通过数值模拟,分析了标的资产和汇率的波动水平以及汇率与标的资产的相关系数对期权的最优执行策略和违约金边界的影响.     

基于通货膨胀和最低保障的DC养老金最优投资

主要研究了通货膨胀和最低保障下的DC养老金的最优投资问题。 首先, 应用伊藤公式得到通胀折现后真实股票价格的微分方程。 然后, 在DC养老金终端财富外部保障约束下, 引入欧式看涨期权, 考虑随机通胀环境下的退休时刻终端财富期望效用最大化问题, 应用鞅方法推导退休时刻以及退休前任意时刻DC养老金最优投资策略的显式解。 最后, 应用蒙特卡洛方法对结果进行数值分析, 分析最低保障对DC养老金最优投资策略的影响。     

考虑即时采购价格的物流服务供应链优化

物流服务市场的不确定性会影响物流服务供应链的服务水平和收益。在考虑随机即时采购价格以及基础物流提供商在正常情况和应急情况下具有不同物流能力投资成本的情形下,引入期权机制研究不确定市场环境下物流服务供应链的优化决策,以提高物流服务供应链柔性和降低市场不确定性带来的风险。构建物流服务供应链的期权契约模型,采用Stackelberg博弈理论和优化算法分析和求得物流服务集成商的最优期权采购和即时采购策略,以及基础物流提供商的最优物流能力投资策略。结果表明即时采购价格将影响基础物流提供商和物流服务集成商的决策。最后通过数值分析研究即时采购价格的不确定程度对物流服务集成商和提供商的优化策略和利润的影响。     

跳-扩散风险模型的最优投资和再保险策略

本文对跳-扩散风险模型,在赔付进行比例再保险,以及盈余投资于无风险资产和风险资产的条件下,研究使得最终财富的指数期望效用最大的最优投资和比例再保险策略.得到最优投资策略和最优再保险策略,以及最大指数期望效用函数的显式表达式,发现最优策略和值函数都受到无风险利率的影响.最后通过数值计算,得到最优投资和比例再保险策略,以及值函数与模型各个参数之间的关系.     

The dynamics of price, quality and productivity improvement decisions

Although quality has received significant attention during the last decades and its economic benefits are beyond any doubt, lots of questions have remained unanswered as to how much, when, and in what to invest to maintain sustainable competitive advantage. A model is introduced here to guide a firm in addressing these questions. The firm produces a single product and operates in a market where monopolistic competition is effective. Demand for the product in the industry depends on both price and performance quality. Increasing productivity knowledge decreases unit production cost, but demand for the company’s product decreases over time, as competitors will be able to offer products with similar performance. Productivity and quality knowledge can be developed through induced and autonomous learning in order to strengthen company position. The paper provides an optimal control formulation of the problem and develops necessary conditions for optimality and characterizes the dynamics of optimal price, quality and investment decisions.     

Optimal portfolio strategies with a liability and random risk: The case of different lending and borrowing rates

This paper deals with two problems of optimal portfolio strategies in continuous time. The first one studies the optimal behavior of a firm who is forced to withdraw funds continuously at a fixed rate per unit time. The second one considers a firm that is faced with an uncontrollable stochastic cash flow, or random risk process. We assume the firm’s income can be obtained only from the investment in two assets: a risky asset (e.g., stock) and a riskless asset (e.g., bond). Therefore, the firm’s wealth follows a stochastic process. When the wealth is lower than certain legal level, the firm goes bankrupt. Thus how to invest in the fundamental problem of the firm in order to avoid bankruptcy. Under the case of different lending and borrowing rates, we obtain the optimal portfolio strategies for some reasonable objective functions that are the piecewise linear functions of the firm’s current wealth and present some interesting proofs for the conclusions. The optimal policies are easy to be operated for any relevant investor.     

目标约束下的投资选择

根据 Markowitz投资组合理论和传统的期望效用理论 ,在效用函数相同的情况下 ,所有的理性投资者都将采用相同的最优投资策略 .但在现实中 ,不同的投资者往往采用不同的投资策略 ,依据传统理论只能认为他们并不都是理性投资者 .本文引入了目标约束后 ,说明了由于不同的投资者具有不同的目标约束 ,所以用传统的期望效用理论无法解释的看似非理性的行为其实却是理性的最优选择 .     

Dynamic investment strategies with demand-side and cost-side risks

Investments in cost reductions are critical for the long run success of companies that operate in dynamic and stochastic market environments. This paper studies optimal investment in cost reductions as a real option under the assumption that a single firm faces two different sources of risk, stochastic demand and input prices. We derive optimal investment strategies for a monopoly as well as a firm in a perfectly competitive market and show that in case of high marginal costs, cost reductions take place earlier in competitive than in monopoly markets. While the existence of an option to invest in cost reductions increases firm value it also increases a firm’s systematic risk. Risk can be smaller in a monopolistic than in a competitive industry.     

Liquidity risk and optimal dividend/investment strategies

In this paper, we study the problem of determining an optimal control on the dividend and investment policy of a firm operating under uncertain environment and risk constraints. We allow the company to make investment decisions by acquiring or selling producing assets whose value is governed by a stochastic process. The firm may face liquidity costs when it decides to buy or sell assets. We formulate this problem as a multi-dimensional mixed singular and multi-switching control problem and use a viscosity solution approach. We numerically compute our optimal strategies and enrich our studies with numerical results and illustrations.     

Strategic optimization in R&D investment

We use d'Aspremont and Jacquemin's strategic optimal R&D investment in a duopoly Cournot competition model to construct myopic optimal discrete and continuous R&D dynamics. We show that for some high initial production costs, the success or failure of a firm is very sensitive to small variations in its initial R&D investment strategies.     

Diversity of firm’s life cycle adapted from the firm’s technology investment decision

The stylized model presented is an optimal control model of technology investment decision of a single product firm. The firm’s technology investment does not have only a long-run positive effect but also a short-run adverse effect on its sales volume. We examine the case of high adverse investment effects where the firm finally leaves the market but we have observed different life cycles till this happens. Depending on the firm’s initial technology stock and sales volume, we compute different firm’s life cycles, which are driven by a trade-off between two strategies: technology versus sales focus strategy. Indifference curves, where managers are indifferent to apply initially technology or sales focus strategies, separate founding conditions of the firm to various classes distinguishable because of the firm’s life cycle.     

基于时滞效应的随机微分投资与比例再保险博弈

金融市场不断发展,激烈的市场竞争使得相对绩效比较在保险机构的业绩评估中占据越来越重要的地位。考虑历史业绩对公司决策的影响,引入时滞效应,研究时滞效应对具有竞争关系公司之间最优投资策略和最优再保险策略的影响。运用随机最优控制和微分博弈理论,针对Cramér-Lundberg模型,得到了均衡投资和再保险策略,给出了值函数的显式解;然后进一步针对近似扩散过程,求得指数效用下均衡投资策略和比例再保险策略的显式表达。通过数值算例,分析了最优均衡策略随模型各重要参数的动态变化。结论显示:保险公司在决策时是否将时滞信息纳入考虑之中将大大影响其投资和再保险行为。保险公司考虑较早时间财富值越多,其投资再保险行为就表现得越趋向于保守和谨慎;与之相反,如果保险公司对行业间的竞争越看重,其投资再保险策略就越倾向于冒险和激进。     

Real options in strategic investment games between two asymmetric firms

This paper examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows. Under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms, we investigate the value of real investment options and strategic interaction of investment decisions. Compared to earlier models that only allow for asymmetry on sunk cost, our model demonstrates a richer set of strategic interactions of entry decisions. We provide a complete characterization of pre-emptive, dominant and simultaneous equilibriums by analyzing the relative value of leader’s and follower’s optimal investment thresholds. In a duopoly market with negative externalities, a firm may reduce loss of real options value by selecting appropriate pre-emptive entry. When one firm has a dominant advantage over its competitor, both the dominant firm and dominated firm enter at their respective leader’s and follower’s optimal thresholds. When the pre-emptive thresholds of both firms happen to coincide, the two firms enter simultaneously. Under positive externalities, firms do not compete to lead.     

The optimal resource portfolio under consumer choice and demand risk for vertically differentiated products

We study the optimal resource portfolio of a firm that sells two vertically differentiated products and utilizes resource flexibility and responsive pricing. We model this decision problem as a two-stage stochastic programming problem with recourse: In the first stage, the firm determines its resource mix and capacities so as to maximize the expected profit under demand uncertainty; in the second stage, uncertainty is resolved and the firm determines its production and pricing decision, constrained by its investment decision. We show that the objective function of this decision problem is not well-behaved (ie, it may have multiple local maxima). Using the concept of Pareto dominance, we reduce the feasible investment region, without loss of optimality, to one in which the objective function is well-behaved everywhere. This reduction allows us to derive the necessary and sufficient conditions for the optimal capacity decision and to gain insights.