Optimal capital accumulation under price uncertainty and costly reversibility

We consider the optimal capital accumulation policy of a competitive firm operating in the presence of decreasing returns to scale, price uncertainty, and costly reversibility of investment. We characterize the optimal accumulation policy and derive the value of the firm by focusing on the marginal investment decision and solving the associated optimal timing problem characterizing the option value of the associated opportunity to either disinvest or acquire a marginal unit of capacity. We also characterize the required exercise premia associated with the optimal policies and demonstrate that hysteresis prevails within this class of accumulation problems as well.     

A model for irreversible investment with construction and revenue uncertainty

This paper presents a model of investment in projects that are characterized by uncertainty over both the construction costs and revenues. Both processes are modeled as spectrally negative Lévy jump-diffusions. The optimal stopping problem that determines the value of the project is solved under fairly general assumptions. It is found that the current value of the benefit-to-cost ratio (BCR) decreases in the frequency of negative shocks to the construction process. This implies that the cost overruns that can be expected if one ignores such shocks are increasing in their frequency. Based on calibrated data, the model is applied to the proposed construction of high-speed rail in the UK and it is found that its economic case cannot currently be made and is unlikely to be met at any time in the next decade. In addition it is found that ignoring construction uncertainty leads to a substantial probability of an erroneous decision being taken.     

Skewness preference,mean–variance and the demand for put options

This paper compares the mean–variance and the mean–variance–skewness approaches to modelling expected utility. Attention is focused on a problem encountered in risk management: determining the optimal demand for a put option hedging the return on an asset with a negatively skewed return distribution. It is demonstrated theoretically that incorporating positive skewness preference into the decision‐maker's objective function typically produces a reduction in the demand for put options when compared with the mean–variance solution. A state‐dependent example is provided to illustrate how a mean–variance–skewness objective can result in a significant reduction in the optimal amount of crop insurance demanded when compared with the mean–variance solution. Copyright © 1999 John Wiley & Sons, Ltd.     

Two-stage optimal control problems and optimality conditions

When an optimal investment decision is studied for a firm whose capital goods are subject to a delivery lag, a control problem with a time-delay argument in the objective function emerges. Such a problem under a set of simple assumptions is shown to be reducible to a two-stage optimal control problem. The significance of this is that familiar tools from standard optimal control theory are applicable to the resulting two-stage problem. Necessary conditions are presented for a general two-stage problem with an adjustable switching time. Some specific results are also obtained for several special cases.     

An analysis of risky financial decisions

A problem of financing uncertain cost of a project is investigated. The paper analyses the allocation and the loss due to the cost uncertainty. Different formulations of the problem are suggested and compared: expected profits, chance constraint maximization and a utility approach. It is shown that even a risk-neutral manager is willing to pay a premium to reduce uncertainty. The two approaches to risk, chance constraint versus concave utility, are shown to be non-equivalent.     

Interest rate, demand and input price uncertainty and the value of firms

In an infinite-horizon inventory model, an increase in interest rate uncertainty increases the value of a firm which has positive value. An increase in input price uncertainty increases the value of the firm. If decisions are made before the realization of demand uncertainty, increased uncertainty about an additive demand shock reduces the value of a price-setting firm with a concave value function, and leaves unchanged or increases the value of a quantity-setting firm. If decisions are made after the realization of demand uncertainty, an increase in the uncertainty of an additive demand shock increases the value of the firm.     

A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.     

The assessment of the expected value of information in the binary decision model

The expected value of information represents the maximum amount the decision maker should spend on inquiry before making a decision. This amount depends upon the accuracy of the information. In many cases of inquiry, prior objective knowledge of the accuracy is not available. This paper presents and compares two methods of subjectively assessing the value of imperfect information in the binary decision model. In the first method, the decision maker provides a likelihood function for the inquiry and hence the probabilities of error. The second method is the preposterior approach, in which the decision maker provides the prior distribution for the posterior probability.     

A real options approach to optimal bidding in construction projects considering volume uncertainty

Building on the numerical solution by Ribeiro et al. (2108), this paper proposes a model to assess the impact of volume uncertainty on construction projects' value and on the optimal bidding price. The model's outcome is the threshold amount for the incremental investment that managers have to undertake in order to resolve the uncertainty regarding the volume of work to be performed. Any amount of investment below the threshold will add value to the project and produces a more competitive bid price. A numerical example is presented, and a sensitivity analysis is performed to the model's most relevant components.     

Optimal consumption under uncertainty,liquidity constraints,and bounded rationality

I study how boundedly rational agents can learn a “good” solution to an infinite horizon optimal consumption problem under uncertainty and liquidity constraints. Using an empirically plausible theory of learning I propose a class of adaptive learning algorithms that agents might use to choose a consumption rule. I show that the algorithm always has a globally asymptotically stable consumption rule, which is optimal. Additionally, I present extensions of the model to finite horizon settings, where agents have finite lives and life-cycle income patterns. This provides a simple and parsimonious model of consumption for large agent based models.     

Extend (r, Q) Inventory Model Under Lead Time and Ordering Cost Reductions When the Receiving Quantity is Different from the Ordered Quantity

This paper investigates the continuous review inventory model involving variable lead time with partial backorders, where the amount received is uncertain. The options of investing in ordering cost reduction is included, and lead time can be shortened at an extra crashing cost. The objective of this article is to simultaneously optimize the order quantity, reorder point, ordering cost and lead time. We first assume that the lead time demand follows a normal distribution and develop an algorithm to find the optimal solution. Then, we relax the assumption of normality to consider a distribution free case where only the mean and standard deviation of lead time demand are known. We apply the minimax distribution free procedure to solve this problem. For both cases, we also show that the objective cost function to be minimized is jointly convex in the decision variables. Furthermore, two numerical examples are given to illustrate the results.     

The role of spatial scale in the timing of uncertain environmental policy

The spatial scale of an environmental problem is dictated by boundaries. Physical boundaries limit the extent of impacts while the scale of decision making creates perceived boundaries beyond which impacts are ignored by decision makers. While it is well understood that uncertainty and irreversibility will alter policy decisions aimed at alleviating environmental impacts, the effect of spatial scales, both physical and perceived, is less understood. When spatial scale is included in a real options model of environmental policy adoption results indicate that the importance and influence of spatial considerations depends on the level of uncertainty, stringency of the proposed policy and flexibility of the policy decision. Recognizing spatial scale may force policy adoption to take place within a window of current damage. When spatial scale is small or uncertainty high, this window for policy adoption can close precluding policy adoption entirely. This undermines well-known results demonstrating that changes in uncertainty will only alter the timing of policy adoption. In other instances, the policy adoption window remains open but the option value increases faster than the benefits of the policy creating a scenario where it is always preferable to delay. Here the inclusion of an option value can prevent adoption of policies that would be adopted according to traditional cost-benefit analysis. In general policy decisions will be most affected by spatial considerations when the spatial scale is small, damage is spreading fast, and the uncertainty in damage spread is high.     

Robustness as a corporate objective under uncertainty

This paper examines the nature of the objective function of the firm when operating under conditions of uncertainty. Robustness is presented as a purposeful maximand for decision making both under conditions of certainty and uncertainty - a robust decision being one in which the decision maker retains the maximum flexibility with regard to future decisions after an initial decision has been made. Its incorporation within a managerial objective function provides a measurable scale for making choices between alternative courses of action, including under conditions of internal organizational conflict and environmental reaction by other decision makers.     

Pricing executive stock options under employment shocks

We obtain explicit expressions for the subjective, objective and market value of perpetual executive stock options (ESOs) under exogenous employment shocks driven by an independent Poisson process. Previously, we obtain the executive's optimal exercise policy from the subjective valuation that is necessary for the objective one, or fair value. The perpetual ESO is compared with the true finite maturity ESO finding that the approximation is reasonably good. To illustrate the usefulness of the objective valuation for accounting purposes, we analyze the statistical distribution of the fair value when there is uncertainty about the employment shock intensity. Finally, the role of ESOs in the design of executives’ incentives is also discussed.     

Price uncertainty and the optimal production-location decision

The integrated production-location decision involves the simultaneous choice of facility design (input mix) and plant location. This paper generalizes earlier work by incorporating price uncertainty and risk preferences into the problem. Properties of the optimal solution are characterized, and detailed comparative statics analyses are performed to identify the effects of price uncertainty, risk preferences, and production structure on the optimal solution. These results, which illuminate the economic mechanics and parametric sensitivity of such decisions, can be useful for developing and evaluating national and local public policies. An example of their potential use is given.     

Optimal requirement allocation among quantity-discount quoting suppliers

We consider a problem motivated by a central purchasing organization for a major office products distributor. This purchasing organization must source a quantity of a particular resale item from a set of capacitated suppliers. In our case each supplier offers an incremental quantity discount purchase price structure. The purchaser’s objective is to obtain a quantity of a required item at minimum cost. The resulting problem is one of allocating order quantities among an approved supply base and involves minimizing the sum of separable piecewise linear concave cost functions. We develop a branch and bound algorithm that arrives at an optimal solution by generating linear knapsack subproblems with feasible solutions to the original problem. This research was partially supported by a 2007 Summer Research Grant awarded to Asoo J. Vakharia.     

Risk, uncertainty, and option exercise

Many economic decisions can be described as an option exercise or optimal stopping problem under uncertainty. Motivated by experimental evidence such as the Ellsberg Paradox, we follow Knight (1921) and distinguish risk from uncertainty. To capture this distinction, we adopt the multiple-priors utility model. We show that the impact of ambiguity on the option exercise decision depends on the relative degrees of ambiguity about continuation payoffs and termination payoffs. Consequently, ambiguity may accelerate or delay option exercise. We apply our results to investment and exit problems, and show that the myopic NPV rule can be optimal for an agent having an extremely high degree of ambiguity aversion.     

Beating the market with a bad predictive model

It is a common misconception that in order to make consistent profits as a trader, one needs to possess some extra information leading to an asset value estimation that is more accurate than that reflected by the current market price. While the idea makes intuitive sense and is also well substantiated by the widely popular Kelly criterion, we prove that it is generally possible to make systematic profits with a completely inferior price-predicting model. The key idea is to alter the training objective of the predictive models to explicitly decorrelate them from the market. By doing so, we can exploit inconspicuous biases in the market maker’s pricing, and profit from the inherent advantage of the market taker. We introduce the problem setting throughout the diverse domains of stock trading and sports betting to provide insights into the common underlying properties of profitable predictive models, their connections to standard portfolio optimization strategies, and the commonly overlooked advantage of the market taker. Consequently, we prove the desirability of the decorrelation objective across common market distributions, translate the concept into a practical machine learning setting, and demonstrate its viability with real-world market data.     

Disclosure Policy in a Mixed Market

This paper investigates the optimal disclosure strategy for private information in a mixed duopoly market, where a state-owned enterprise (SOE) and a joint-stock company compete to supply products. I construct a model where the two firms compete in either quantity or price, and uncertainty is associated with either marginal cost or market demand. The model identifies the optimal disclosure strategies that constitute a perfect Bayesian equilibrium by type of competition and uncertainty. In Cournot competition, both firms disclose information under cost uncertainty, while only the SOE or neither firm discloses information under demand uncertainty. Alternatively, in Bertrand competition, only the joint-stock company discloses information under cost uncertainty or demand uncertainty. Recently, developed countries have required the same level of disclosure standards for SOEs as for ordinary joint-stock companies. The findings described in this paper warn that such mandatory disclosure by SOEs can trigger a reaction by joint-stock companies, putting the economy at risk of a reduction in welfare.     

Stochastic endogenous time preference

Preference for flexibility arises inherently in sequential decision making. However, a majority of the literature has limitations to capture a changing preference for flexibility across time in the sense that such an attitude is independent of past actions. This study incorporates the histories of past actions into an infinite-horizon extension of Dekel et al. (2001) and models a decision maker whose attitude toward flexibility evolves over time from the uncertainty of future time preference or discount factors. Moreover, we provide behavioral comparisons of the degree of patience across different histories and characterize the shift of subjective beliefs about discount factors in the sense of an increasing convex and concave stochastic order.