Technology choice under several uncertainty sources

We analyze a model of irreversible investment with two sources of uncertainty. A risk-neutral decision maker has the choice between two mutually exclusive projects under input price and output price uncertainty. We propose a complete study of the shape of the rational investment region and we prove that it is never optimal to invest when the alternative investments generate the same payoff independently of its size. A key feature of this bidimensional degree of uncertainty is thus that the payoff generated by each project is not a sufficient statistic to make a rational investment. In this context, our analysis provides a new motive for waiting to invest: the benefits associated with the dominance of one project over the other. As an illustration, we apply our methodology to power generation under uncertainty.     

Renewable energy investments under different support schemes: A real options approach

This paper adopts a real options approach to analyze investment timing and capacity choice for renewable energy projects under different support schemes. The main purpose is to examine investment behavior under the most extensively employed support schemes, namely, feed-in tariffs and renewable energy certificate trading. We consider both multiple sources of uncertainty under each support scheme and uncertainty with respect to any change of support scheme, and we obtain both analytical (when possible) and numerical solutions. In a Nordic case study based on wind power, we find that the feed-in tariff encourages earlier investment. Nevertheless, as investment has been undertaken, renewable energy certificate trading creates incentives for larger projects. In our baseline scenario and taking the fixed feed-in tariff as a base, the revenue required to trigger investments is 61% higher with renewable certificates. At the same time, investment capacity is 61% higher.     

基于回收期的科技创新项目决策模型分析

回收期方法是一种常用的评价方法.本文通过实物期权思想,对在不确定性下的科技创新项目,论证了回收期方法是合理的,通过本文的计算分析可知,较短的回收期隐含着较少的等待价值,也隐含着较高的单位资本回报.因此,利用回收期方法评价科技创新项目,不仅能得出与NPV方法评价的同样结论,而且还给投资者更多的信息,如几年之内可望收回投资.这对于资本不太雄厚的投资者来说更具有实际的意义,而对于资本雄厚的投资者也提供了能获得更多回报的投资决策评价方法.     

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.     

Hysteresis effects under CIR interest rates

Most decision making research in real options focuses on revenue uncertainty assuming discount rates remain constant. However, for many decisions revenue or cost streams are relatively static and investment is driven by interest rate uncertainty, for example the decision to invest in durable machinery and equipment. Using interest rate models from Cox et al. (1985b), we generalize the work of Ingersoll and Ross (1992) in two ways. Firstly, we include real options on perpetuities (in addition to zero coupon cash flows). Secondly, we incorporate abandonment or disinvestment as well as investment options, and thus model interest rate hysteresis (parallel to revenue uncertainty in Dixit (1989a)). Under stochastic interest rates, economic hysteresis is found to be significant, even for small sunk costs.     

奈特不确定条件下企业有成本可逆投资策略研究

风险是企业投资决策关键影响因素之一,采纳奈特不确定性来刻画风险,并在此基础上构建了模糊规避偏好和投资有成本可逆条件下企业投资决策模型.模型结果表明企业最优投资策略为双阈值策略:企业增加投资以避免资本边际收益大于上限阈值,削减资本存量以避免资本边际收益低于下限阈值,当资本边际收益处于上下限阈值之间时,企业既不增加投资也不削减资本.比较静态分析显示奈特不确定性增加会降低最优投资策略上下限阈值范围.     

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.     

Supplier quality improvement: The value of information under uncertainty

We consider supplier development decisions for prime manufacturers with extensive supply bases producing complex, highly engineered products. We propose a novel modelling approach to support supply chain managers decide the optimal level of investment to improve quality performance under uncertainty. We develop a Poisson–Gamma model within a Bayesian framework, representing both the epistemic and aleatory uncertainties in non-conformance rates. Estimates are obtained to value a supplier quality improvement activity and assess if it is worth gaining more information to reduce epistemic uncertainty. The theoretical properties of our model provide new insights about the relationship between the degree of epistemic uncertainty, the effectiveness of development programmes, and the levels of investment. We find that the optimal level of investment does not have a monotonic relationship with the rate of effectiveness. If investment is deferred until epistemic uncertainty is removed then the expected optimal investment monotonically decreases as prior variance increases but only if the prior mean is above a critical threshold. We develop methods to facilitate practical application of the model to industrial decisions by a) enabling use of the model with typical data available to major companies and b) developing computationally efficient approximations that can be implemented easily. Application to a real industry context illustrates the use of the model to support practical planning decisions to learn more about supplier quality and to invest in improving supplier capability.     

不确定环境下基于资金约束的技术授权策略

技术创新的价值实现需要后续的商业化开发,市场需求不确定会影响商业化投资的价值评估,在企业商业化受到资金约束时如果进行资金筹集就会有一定困难,而合理设计的授权合约这时可以作为项目的融资途径之一。本文研究了企业的最优授权策略在无资金约束时和资金约束时的差异,试图通过技术授权合约的设计进行筹资,发现利用授权合约的预付金可以满足部分融资需要,但是使用授权合约融资的成本较高,影响融资额度的主要因素包括接受授权企业的研发成本、市场需求的预期、单位产品税的承诺等。     

Optimal spot market inventory strategies in the presence of cost and price risk

We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time. The firm’s goal is to maximize expected discounted profit over the period, where profit consists of the revenue from selling goods to meet demand, on the spot market, or in salvage, minus the cost of buying goods, and transaction, penalty, and holding costs. We first show that this optimization problem is equivalent to a two-dimensional singular control problem. We then use a recently developed control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two-threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then passively waiting for demand. In these experiments, we observe that as price volatility increases, the value of actively managing inventory increases until some limit is reached.     

An examination of the role of price insurance products in stimulating investment in agriculture supply chains for sustained productivity

This study examines how managing risk by introducing commodity price insurances may improve the likelihood of increased investment in agri-food supply chains. A model is introduced which shows how insurance products on index prices can reduce the uncertainty of the impact of investment, and also how lower investment can generate the same impact as a higher investment. To show our results, we use two different frameworks which include total profit (Pareto optimal) and Stackelberg game setups. The results demonstrate that in both frameworks the investment will have a greater impact when an insurance product is present. By implication, the study presents an encouraging message to the insurance industry to introduce products to secure supply chain actors’ revenue leading to an increase in investment rate. Consequently, the study offers insight into how the role of traditional government subsidies for protecting farmers, particularly the small to medium-sized farms, may be revisited by replacing some of the existing subsidisation policies with revenue insurance.     

在未来收益不确定下的期权定价模型

§ 1　 IntroductionAt present,some high-technology(high-tech) firms such as information,software,pharmaceutical et al,are rapidly growing at home and abroad.The firm' s stock price hasbeen bid upward irrationally by individual day traders.Some managers see the currentfren-zy as a spectacularexample ofmarketbubble.The marketbubble can' tbe explained by theaverage rate of growth,butithas reacted on the developmentprospect of high-tech firms.Existing net cash flow method cannot properly capture …     

客源充足情境下的customer-intensive服务策略研究

在customer-intensive服务中服务速度越慢,顾客的效用就越高,然而等待时间也随之变长;而服务商则需对服务速度和价格进行决策,以求获得最优收益。本文基于客源丰富的服务垄断商对此问题采用M/M/1排队模型进行了研究,将顾客成本细分为时间成本和焦虑成本,给出了最优服务速度和价格。研究发现,单位焦虑成本的增加造成了服务商收益的减少,但对收益的影响要小于单位时间成本。最后,提出了服务商投入一定的服务成本来减少焦虑成本的策略,以达到获取更高收益的目的,并证明了策略的有效性。     

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.     

Investment in electric energy storage under uncertainty: a real options approach

In this paper we develop a real options approach to evaluate the profitability of investing in a battery bank. The approach determines the optimal investment timing under conditions of uncertain future revenues and investment cost. It includes time arbitrage of the spot price and profits by providing ancillary services. Current studies of battery banks are limited, because they do not consider the uncertainty and the possibility of operating in both markets at the same time. We confirm previous research in the sense that when a battery bank participates in the spot market alone, the revenues are not sufficient to cover the initial investment cost. However, under the condition that the battery bank also can receive revenues from the balancing market, both the net present value (NPV) and the real options value are positive. The real options value is higher than the NPV, confirming the value of flexible investment timing when both revenues and investment cost are uncertain.     

Robust assortment optimization using worst-case CVaR under the multinomial logit model

We consider robust assortment optimization problems with partial distributional information of parameters in the multinomial logit choice model. The objective is to find an assortment that maximizes a revenue target using a distributionally robust chance constraint, which can be approximated by the worst-case Conditional Value-at-Risk. We show that our problems are equivalent to robust assortment optimization problems over special uncertainty sets of parameters, implying the optimality of revenue-ordered assortments under certain conditions.     

A note on issues of over-conservatism in robust optimization with cost uncertainty

We identify and discuss issues of hidden over-conservatism in robust linear optimization, when the uncertainty set is polyhedral with a budget of uncertainty constraint. The decision-maker selects the budget of uncertainty to reflect his degree of risk aversion, i.e. the maximum number of uncertain parameters that can take their worst-case value. In the first setting, the cost coefficients of the linear programming problem are uncertain, as is the case in portfolio management with random stock returns. We provide an example where, for moderate values of the budget, the optimal solution becomes independent of the nominal values of the parameters, i.e. is completely disconnected from its nominal counterpart, and discuss why this happens. The second setting focusses on linear optimization with uncertain upper bounds on the decision variables, which has applications in revenue management with uncertain demand and can be rewritten as a piecewise linear problem with cost uncertainty. We show in an example that it is possible to have more demand parameters equal their worst-case value than what is allowed by the budget of uncertainty, although the robust formulation is correct. We explain this apparent paradox.     

On the optimality of threshold control in queues with model uncertainty

We consider a single-stage queuing system where arrivals and departures are modeled by point processes with stochastic intensities. An arrival incurs a cost, while a departure earns a revenue. The objective is to maximize the profit by controlling the intensities subject to capacity limits and holding costs. When the stochastic model for arrival and departure processes are completely known, then a threshold policy is known to be optimal. Many times arrival and departure processes can not be accurately modeled and controlled due to lack of sufficient calibration data or inaccurate assumptions. We prove that a threshold policy is optimal under a max–min robust model when the uncertainty in the processes is characterized by relative entropy. Our model generalizes the standard notion of relative entropy to account for different levels of model uncertainty in arrival and departure processes. We also study the impact of uncertainty levels on the optimal threshold control.     

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.