"Irreversible Investment and Knightian Uncertainty"

When firms decide about irreversible investment, they may not have perfect confidence about their perceived probability measure describing future uncertainty. They may think other probability measures perturbed from the original one are also probable. Uncertainty characterized by not a single probability measure but a set of probability measures is called Knightian uncertainty. The effect of Knightian uncertainty on the value of irreversible investment opportunity is shown to be drastically different from that of the traditional uncertainty in the form of risk. Specifically, an increase in Knightian uncertainty decreases the value of investment opportunity while an increase in risk increases it.

Investment Model Uncertainty and Fair Pricing

Modern investment theory takes it for granted that a Security Market Line (SML) is as certain as its "corresponding" Capital Market Line. (CML). However, it can be easily demonstrated that this is not the case. Knightian non-probabilistic, information gap uncertainty exists in the security markets, as the bivariate "Galton's Error" and its concomitant information gap proves (Journal of Banking & Finance, 23, 1999, 1793-1829). In fact, an SML graph needs (at least) two parallel horizontal beta axes, implying that a particular mean security return corresponds with a limited Knightian uncertainty range of betas, although it does correspond with only one market portfolio risk volatility. This implies that a security' risk premium is uncertain and that a Knightian uncertainty range of SMLs and of fair pricing exists. This paper both updates the empirical evidence and graphically traces the financial market consequences of this model uncertainty for modern investment theory. First, any investment knowledge about the securities risk remains uncertain. Investment valuations carry with them epistemological ("modeling") risk in addition to the Markowitz-Sharpe market risk. Second, since idiosyncratic, or firm-specific, risk is limited-uncertain, the real option value of a firm is also limited-uncertain This explains the simultaneous coexistence of different analyst valuations of investment projects, particular firms or industries, included a category "undecided." Third, we can now distinguish between "buy", "sell" and "hold" trading orders based on an empirically determined collection of SMLs, based this Knightian modeling risk. The coexistence of such simultaneous value signals for the same security is necessary for the existence of a market for that security! Without epistemological investment uncertainty, no ongoing markets for securities could exist. In the absence of transaction costs and other inefficiencies, Knightian uncertainty is the necessary energy for market trading, since it creates potential or perceived arbitrage (= trading) opportunities, but it is also necessary for investors to hold securities. Knightian uncertainty provides a possible reason why the SEC can't obtain consensus on what constitutes "fair pricing." The paper also shows that Malkiel's recommended CML-based investments are extremely conservative and non-robust.capital market line, security market line, beta, investments, decision-making, Knightian uncertainty, robustness, information-gap, Galton's Error, real option value

Dark Clouds or Silver Linings? Knightian Uncertainty and Climate Change

This paper examines the impact of Knightian uncertainty upon optimal climate policy through the prism of a continuous-time real option modelling framework. We analytically determine optimal intertemporal climate policies under ambiguity. Additionally, numerical simulations are provided to illustrate the properties of the model. The results indicate that increasing Knightian uncertainty accelerates climate policy, i.e. policymakers become more reluctant to postpone the timing of climate policies into the future.climate change, Knightian uncertainty, ê ambiguity, real options

Irreversibilities and the Optimal Timing of Environmental Policy under Knightian Uncertainty

In this paper, we consider a problem in environmental policy design by applying optimal stopping rules. The purpose of this paper is to analyze the optimal timings at which the government should adopt environmental policies to deal with increases in greenhouse gas concentrations and to reduce emissions of SO2 or CO2 under the continuous-time Knightian uncertainty. Furthermore, we analyze the effects of increases in Knightian uncertainty on optimal environmental policies and the reservation value.

Collective Risk Management in a Flight to Quality Episode

We present a model of optimal intervention in a flight to quality episode. The reason for intervention stems from a collective bias in agents' expectations. Agents in the model make risk management decisions with incomplete knowledge. They understand their own shocks, but are uncertain of how correlated their shocks are with systemwide shocks, treating the latter uncertainty as Knightian. We show that when aggregate liquidity is low, an increase in uncertainty leads agents to a series of protective actions -- decreasing risk exposures, hoarding liquidity, locking-up capital -- that reflect a flight to quality. However, the conservative actions of agents leave the aggregate economy over-exposed to negative shocks. Each agent covers himself against his own worst-case scenario, but the scenario that the collective of agents are guarding against is impossible. A lender of last resort, even if less knowledgeable than private agents about individual shocks, does not suffer from this collective bias and finds that pledging intervention in extreme events is valuable. The intervention unlocks private capital markets.

Creating Products in the Absence of Markets: A Robust Design Approach

The purpose of this study is to examine how firms deal with a situation of true uncertainty about their potential markets and technologies. Specifically, we ask how firms can create products when the corresponding market does not exist. Design/methodology/approach : This paper is based on a longitudinal study of a high-tech firm, combined with analysis of existing theory in Product Design and Entrepreneurship. Findings – Markets and products are usually a defining choice made early on by firms in their strategic process. Such a choice guides their development by providing a ‘stable concept' to which decisions can be related to. When markets do not exist yet, however, this approach is not effective: Early choice of products and markets limits firms' flexibility by constraining their ability and willingness to adapt, while fundamental new technical and market information is likely to emerge during the project that will prove the initial assumptions wrong."New Product Development";"uncertainty";"high-technology venture"

Creating Products in the Absence of Markets: A Robust Design Approach

Purpose - The purpose of this study is to examine how firms deal with a situation of true uncertainty about their potential markets and technologies. Specifically, we ask how firms can create products when the corresponding market does not exist. Design/methodology/approach – This paper is based on a longitudinal study of a high-tech firm, combined with analysis of existing theory in Product Design and Entrepreneurship. Findings – Markets and products are usually a defining choice made early on by firms in their strategic process. Such a choice guides their development by providing a ‘stable concept' to which decisions can be related to. When markets do not exist yet, however, this approach is not effective: Early choice of products and markets limits firms' flexibility by constraining their ability and willingness to adapt, while fundamental new technical and market information is likely to emerge during the project that will prove the initial assumptions wrong. We show an alternative approach where products and markets actually result from a generic process of products and markets exploration driven by the firm. We suggest that this approach forms a robust design in that it allows the firm to deal with the uncertainty by simultaneously developing its products and exploring markets, while preserving the flexibility to adapt to the changing environment. Practical implications – The practical implication of this paper is to suggest an alternative approach to deliberate planning in high-tech ventures. With this approach, rather than markets and products, strategy defines a market and technology exploration process. Originality/value – The paper is original in three ways: 1) It links the product design and market exploration processes in high-tech firm development; 2) It is based on an in-depth longitudinal study; and 3) It results from an academic-practitioner collaborative work.New Product Development; uncertainty; high-technology venture.

Real Options under Choquet-Brownian Ambiguitys

Real options models characterized by the presence of “ambiguity” (or “Knightian uncertainty”) have been recently proposed. But based on recursive multiple-priors preferences, they typically describe ambiguity through a range of Geometric Brownian motions and solve it by application of a maxmin expected utility criterion among them (worst case). This reduces acceptable individual preferences to the single case of an extreme form of pessimism. In contrast, by relying on dynamically consistent “Choquet-Brownian” motions to represent the ambiguous cash flows expected from a project, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for, improving the explanatory and application potentials of these appealing expanded real options models. In the case of a perpetual real option to invest, ambiguity aversion may delay the moment of exercise of the option, while the opposite holds true for an ambiguity seeking decision maker. Furthermore, an intricate relationship between risk and ambiguity appears strikingly in our model.

Real Options under Choquet-Brownian Ambiguity

Real options models characterized by the presence of ambiguity have been recently proposed. But based on recursive multiple-priors approaches to solve ambiguity, these seminal models reduce individual preferences to extreme pessimism by considering only the worst case scenario. In contrast, by relying on dynamically consistent Choquet-Brownian motions to model the dynamics of ambiguous expected cash flows, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for. In the case of a perpetual real option to invest, ambiguity aversion delays the moment of exercise of the option, while the opposite holds true for an ambiguity lover.Real Options; Ambiguity; Irreversible investment; Optimal stopping; Knightian uncertainty; Choquet-Brownian motions

Price-Based vs. Quantity-Based Environmental Regulation under Knightian Uncertainty: An Info-Gap Robust Satisficing Perspective

Conventional wisdom among environmental economists is that the relative slopes of the marginal social benefit and marginal social cost functions determine whether a price-based or quantity-based environmental regulation leads to higher expected social welfare. We revisit the choice between price-based vs. quantity-based environmental regulation under Knightian uncertainty; that is, when uncertainty cannot be modeled with known probability distributions. Under these circumstances, the policy objective cannot be to maximize the expected net benefits of emissions control. Instead, we evaluate an emissions tax and an aggregate abatement standard in terms of maximizing the range of uncertainty under which the welfare loss from error in the estimates of the marginal benefits and costs of emissions control can be limited. The main result of our work is that the same criterion involving the relative slopes of the marginal benefit and cost functions determines whether price-based or quantity-based control is more robust to unstructured uncertainty. Hence, not only does the relative slopes criterion lead to the policy that maximizes the expected net benefits of control under structured uncertainty, it also leads to the policy that maximizes robustness to unstructured uncertainty.emissions control, environmental regulation, info-gap, Knightian uncertainty, robustness, satisficing