Knightian Uncertainty Research Articles

Stability of stochastic Hopfield neural networks driven by [formula omitted]-Brownian motion with time-varying and distributed delays

In this paper, pth exponential stability and quasi-surely exponential stability of stochastic Hopfield neural networks driven by G-Brownian motion are investigated. Under a sublinear expectation framework, we give several lemmas related to the Halanay inequality and the Burkholder-Davis-Gundy ineqaulity. Our stability results is based on the class of the multidimensional Halanay inequalities, as well as the Burkholder-Davis-Gundy inequalities. The main originality lies in the fact that we consider Knightian uncertainty of the theory model of stochastic Hopfield neural networks. Finally, two numerical examples are presented to illustrate our new theory.

Asset prices in a labor search model with confidence shocks

This paper studies a labor search model with agents who are averse to ambiguity (Knightian uncertainty). Shocks to confidence about future productivity are modeled as changes in ambiguity. Using the Survey of Professional Forecasters data, I find that confidence shocks help explain the equity premium and the stock market volatility, including their term structure. Ambiguity amplifies the response of the economy to productivity shocks, helping the model produce more realistic dynamics of unemployment, vacancies, labor market tightness, stock prices, and returns. Returns in the model are predictable with price-dividend ratios; both returns and dividends are predictable with unemployment, like in the data. Two extensions consider shocks to bargaining power and to separation rate and find similar implications of ambiguity about these shocks.

Ambiguity and self-protection: evidence from social distancing under the COVID-19 pandemic.

This paper studies how people make decisions over preventive behaviors under ambiguity (i.e., Knightian uncertainty) where they do not even know the probability of a loss. In the context of the current COVID-19 pandemic, scientific uncertainty makes it hard to evaluate not only whether one will be infected, but also probabilities such as the infection rate. We constructed a simple model and demonstrated how its effect was heterogeneous depending on ambiguity-attitudes. Motivated by the model, we further conducted a survey experiment in Japan where we manipulated the information regarding scientific uncertainty on COVID-19. We found that higher ambiguity induced by scientific uncertainty increased the level of social distancing among ambiguity-loving people, but such evidence was nonexistent for ambiguity-averse counterparts.Supplementary InformationThe online version contains supplementary material available at 10.1007/s42973-022-00120-3.

From Knightian uncertainty to real‐structuredness: Further opening the judgment black box

AbstractResearch SummaryEntrepreneurial judgment remains a concept that resembles a black box. This article attempts to further open that black box by developing a dimensionalization of types of judgment. To achieve this, it joins recent efforts to explicitly link entrepreneurship to Simonian themes by integrating the notion of decision problem structures into the judgment‐based approach (JBA) to entrepreneurship. This article proposes a more comprehensive and nuanced approach to judgment in the face of decision problems we label “real‐structured.” Extending the JBA comes with several important implications: It uncovers additional entrepreneurial knowledge problems, provides new insights for both economic organization and judgment communicability, and informs research on entrepreneurial success and failure. It also sheds new light on the controversy over the relationship between effectuation and judgment.Managerial SummaryWhen taking decisions, entrepreneurs cannot know how the future will pan out. Those decisions are made under conditions of uncertainty and only time will tell whether they prove astute or otherwise. The uncertainty of the future leads entrepreneurs to exercise judgment based on their individual beliefs and to act accordingly. The components of that entrepreneurial judgment remain rather underexplored. The purpose of this article is to dig deeper into, and thereby improve, the understanding of entrepreneurial judgment. The main result of this article is a four‐part dimensionalization of judgment, covering entrepreneurial (sub‐)judgments on the effects incurred by action, the appraisal of action alternatives, the goals underlying action, and resolving the decision problem.

Stochastic representation under g-expectation and applications: The discrete time case

In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we investigate a new approach to the optimal stopping problem under g-expectation and the related pricing of American options under Knightian uncertainty. Our results are also applied to a (non-linear) Skorokhod-type obstacle problem.

Robustly Optimal Monetary Policy in a Behavioral Environment

Abstract This paper studies robustly optimal monetary policy with myopic agents in a behavioral New Keynesian model. The central bank is assumed to have Knightian uncertainty about the degree of myopia and the degree of price stickiness. We show that, under uncertainty about myopia, the Brainard’s attenuation principle holds under commitment and discretion, while, under uncertainty on price stickiness, alone or in addition to myopia, monetary policy becomes more aggressive. Welfare evaluation shows significant gains from a robust conduct of monetary policy when the model is distorted.

Model Uncertainty: A Reverse Approach

In robust finance, Knightian uncertainty is often captured by sets of probability measures on the future states of the world. If these measures are nondominated, this usually comes at the cost of losing tractability, and advanced functional-analytic tools are often not available anymore. This tends to be mitigated by ad hoc assumptions that guarantee a certain degree of tractability, for instance concerning the aggregation of consistent random variables. The present paper instead investigates from a reverse perspective what implications the validity of certain functional-analytic tools has. In this vein, we categorise the Kreps-Yan property, robust variants of the Brannath-Schachermayer Bipolar Theorem and the Grothendieck Lemma, and uncertain volatility models. By doing so, we also uncover connections to robust statistics.

Pricing interest rate derivatives under volatility uncertainty

In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility uncertainty. The uncertainty about the volatility is modeled by a G-Brownian motion, which drives the forward rate dynamics. The absence of arbitrage is ensured by a drift condition. Such a setting leads to a sublinear pricing measure for additional contracts, which yields either a single price or a range of prices and provides a connection to hedging prices. Similar to the forward measure approach, we define the forward sublinear expectation to simplify the pricing of cashflows. Under the forward sublinear expectation, we obtain a robust version of the expectations hypothesis, and we show how to price options on forward prices. In addition, we develop pricing methods for contracts consisting of a stream of cashflows, since the nonlinearity of the pricing measure implies that we cannot price a stream of cashflows by pricing each cashflow separately. With these tools, we derive robust pricing formulas for all major interest rate derivatives. The pricing formulas provide a link to the pricing formulas of traditional models without volatility uncertainty and show that volatility uncertainty naturally leads to unspanned stochastic volatility.

Covid-19 Policy Convergence in Response to Knightian Uncertainty.

Domestic policy responses to COVID-19 were remarkably consistent during the early days of the pandemic. What explains this policy convergence? Our formal model suggests that the novel character of COVID-19 produced a period of maximum policy uncertainty, incentivizing political actors to converge on a common set of policies to minimize their exposure to electoral punishment. This convergence is likely to break down as policy feedback produces opinion divergence among experts and the public and as politicians recalculate the costs and benefits of various policy responses and under some conditions facing incentives to adopt extreme policies.

A strategy map as a framework of a shared mental model for interactive control systems

Nowadays, companies operate in an extremely turbulent environment with conditions of substantial gaps in knowledge about future events (the Knightian uncertainty). Therefore, there is a need for more flexible management control systems. Referring to Simons’ levers of control (LOC) framework, now there is a need to use more extensively belief systems and interactive control systems that would enable the organizational learning process. The aim of this paper is to discuss the role of a strategy map as a framework of a shared mental model for interactive control systems in the context of increasing uncertainty. This article is a review-based study and suggests some preliminary proposals for further research. The review covers the literature on management control systems, levers of control (in the including of interactive controls), balanced scorecards, strategy maps, mental models, and organizational learning. The review is mainly qualitative; however, it is supported to some extent by quantitative bibliometric analysis. This co-word analysis applies VOSviewer v.1.6.17 software. The situation of increasing Knightian uncertainty calls for the more extensive use of interactive control systems. A strategy map fits this new demand - it enables understanding strategic assumptions, structuring the problems, discussing, and gaining knowledge. Therefore, it facilitates innovations, organizational learning, and refining strategies in an ongoing process. A strategy map can be seen as a cognitive mapping tool. It is a set of hypotheses that can be empirically tested through strategy implementation, thereby enabling strategic learning (including so-called double-loop feedback learning). Such a double-loop learning mechanism allows for the iterative crafting of an organizational strategy that could be more resilient in a turbulent environment. To be the basis of an interactive control system, it is crucial for the “buy-in” of the strategy map by employees. Thus, there is a great role in the convergence of mental models of an organization’s members as a result of “strategic conversation”. The product of such an organizational learning process is a common, shared mental model. This model must be developed, disseminated in the organization and accepted by employees, and then refined through active learning.

A strategy map as a framework of a shared mental model for interactive control systems

Nowadays, companies operate in an extremely turbulent environment with conditions of substantial gaps in knowledge about future events (the Knightian uncertainty). Therefore, there is a need for more flexible management control systems. Referring to Simons’ levers of control (LOC) framework, now there is a need to use more extensively belief systems and interactive control systems that would enable the organizational learning process. The aim of this paper is to discuss the role of a strategy map as a framework of a shared mental model for interactive control systems in the context of increasing uncertainty. This article is a review-based study and suggests some preliminary proposals for further research. The review covers the literature on management control systems, levers of control (in the including of interactive controls), balanced scorecards, strategy maps, mental models, and organizational learning. The review is mainly qualitative; however, it is supported to some extent by quantitative bibliometric analysis. This co-word analysis applies VOSviewer v.1.6.17 software. The situation of increasing Knightian uncertainty calls for the more extensive use of interactive control systems. A strategy map fits this new demand - it enables understanding strategic assumptions, structuring the problems, discussing, and gaining knowledge. Therefore, it facilitates innovations, organizational learning, and refining strategies in an ongoing process. A strategy map can be seen as a cognitive mapping tool. It is a set of hypotheses that can be empirically tested through strategy implementation, thereby enabling strategic learning (including so-called double-loop feedback learning). Such a double-loop learning mechanism allows for the iterative crafting of an organizational strategy that could be more resilient in a turbulent environment. To be the basis of an interactive control system, it is crucial for the “buy-in” of the strategy map by employees. Thus, there is a great role in the convergence of mental models of an organization’s members as a result of “strategic conversation”. The product of such an organizational learning process is a common, shared mental model. This model must be developed, disseminated in the organization and accepted by employees, and then refined through active learning.

Optimal consumption with Hindy–Huang–Kreps preferences under nonlinear expectations

AbstractWe study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent’s preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a backward equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.

Ambiguity aversion and amplification of financial crisis

We introduce Knightian uncertainty into a standard global game framework to propose a new amplification mechanism of financial crises. In the model, ambiguity-averse speculators are uncertain about the accuracy of a public signal. They shift more weight to the public signal when it is deteriorating. In the equilibrium, a public signal cut-off characterises the coordination attack against the regime. Below (above) the cut-off, there is a weak (strong) regime in which the public signal is more (less) pronounced. For an outside observer, there is an asymmetric amplification of the financial crisis. We derive the magnitude of amplification and study its property. To enhance financial stability, a policymaker may clarify the source of a public rumour.

The impact of operational delay on irreversible investment under Knightian uncertainty

Lags between investing in a venture and when it comes into operation have a significant effect on the operative capacity of a firm. However, with a few exceptions, such lags are ignored in the modelling of irreversible investment under uncertainty. In this paper I examine the impact such lags have on the optimal investment strategy of a firm in the context of Knightian uncertainty (KU) and an ambiguity-averse investor. I find the effect of such lags to be significant in this context and, for high enough levels of KU, its widely reported negative impact on the threshold is reversed entirely by the delay. Furthermore, when KU and lags are jointly incorporated into a problem of irreversible investment under uncertainty, volatility impacts the NPV from investing (in the absence of either, it has no impact).

Optimal Multiple Stopping Problems Under g-expectation

In this paper, we study the optimal multiple stopping problem under Knightian uncertainty both under discrete-time case and continuous-time case. The Knightian uncertainty is modeled by a single real-valued function g, which is the generator of a kind of backward stochastic differential equations. We show that the value function of the multiple stopping problem coincides with the one corresponding to a new reward sequence or process. For the discrete-time case, this problem can be solved by an induction method which is a straightforward generalization of the single stopping theory. For the continuous-time case, we furthermore need to establish the continuity of the new reward family. This result can be applied to the pricing problem for swing options in financial markets, which gives the holder of this contract at least two times rights to exercise it.

OPTIMAL PORTFOLIO CHOICE WITH CRASH RISK AND MODEL AMBIGUITY

In this paper, we consider a continuous time portfolio optimization problem that includes the possibility of a crash scenario as well as parameter uncertainty. To do this, we combine the worst-case scenario approach, introduced by Korn & Wilmott (2002) with a model ambiguity approach that is also based on Knightian uncertainty. In our model, the crash scenario occurs at the worst possible time for the investor, which also implies that there can be no crash at all. For the modeling of the parameter uncertainty, we choose a general definition of the sets of possible drift and volatility parameters, conditioned by the solution of an optimization problem. In addition, these sets may be different in the pre-crash and post-crash market. We solve this portfolio problem and then consider two particular examples with box uncertainty and ellipsoidal drift ambiguity.

MODELING ENTREPRENEURIAL INVESTMENT DECISIONS IN THE CYBERSECURITY SPHERE UNDER AMBIGUITY

Most economic decisions are made under uncertainty, and decision-makers, particularly entrepreneurs are conscious of external factors that affect their decisions yet are out of their control. However, making the best predictions, these factors or variables will determine the effectiveness of their decisions, which are also influenced by political, environmental, technological and other developments during the course of the investment. In this context, given the high-level uncertainty in the cyber environment and the stochastic nature of cyber threats, it is essential to analyze the uncertain and unpredictable market conditions, study the factors, affecting irreversible investments and define the optimal timing of investment decisions. The standard investment models presuppose that the entrepreneur has an extreme aversion to uncertainty, i.e., mostly considering the worst-case scenarios without ambiguity. This article presents an entrepreneurial investment decision-making model and demonstrates the significance of an entrepreneur's attitude towards Knightian uncertainty (ambiguity) when making investment decisions in the field of cyber security. The model introduces both complete ambiguity-aversion and ambiguity-loving cases․ The numerical example demonstrates the effects of changes in the perceived level of ambiguity and the entrepreneur’s attitude toward ambiguity on the expected value of an investment project. Accordingly, the entrepreneur invests if and only if the expected profit level exceeds the critical level of current profits (threshold), otherwise the investment will not be undertaken.

A survey comparative analysis of cartesian and complexity science frameworks adoption in financial risk management of Zimbabwean banks

<abstract> <p>Traditionally, financial risk management is examined with cartesian and interpretivist frameworks. However, the emergence of complexity science provides a different perspective. Using a structured questionnaire completed by 120 Risk Managers, this paper pioneers a comparative analysis of cartesian and complexity science theoretical frameworks adoption in sixteen Zimbabwean banks, in unique settings of a developing country. Data are analysed with descriptive statistics. The paper finds that overally banks in Zimbabwe are adopting cartesian and complexity science theories regardless of bank size, in the same direction and trajectory. However, adoption of cartesian modeling is more comprehensive and deeper than complexity science. Furthermore, due to information asymmetries, there is diverging modeling priorities between the regulator and supervisor. The regulator places strategic thrust on Knightian risks modeling whereas banks prioritise ontological, ambiguous and Knightian uncertainty measurement. Finally, it is found that complexity science and cartesianism intersect on market discipline. From these findings, it is concluded that complexity science provides an additional dimension to quantitative risk management, hence an integration of these two perspectives is beneficial. This paper makes three contributions to knowledge. First, it adds valuable insights to theoretical perspectives on Quantitative Risk Management. Second, it provides empirical evidence on adoption of two theories from developing country perspective. Third, it offers recommendations to improve Quantitative Risk Management policy formulation and practice.</p> </abstract>

Bringing People to the Table in New Ventures: An Effectual Approach

When building new ventures, entrepreneurs confront the three problems of Knightian uncertainty, goal ambiguity, and isotropy. The literature on effectuation offers a framework for action, interaction, and reaction within the prediction control space that can help entrepreneurs tackle the above three problems. In this article, we offer a framework consisting of four approaches to negotiation that populate the prediction‐control space, namely, Pitch, Help, Deal, and (Effectual) Ask. While we emphasize the effectual quadrant, we examine all four from a practical perspective informed by theory, while forging important connections with established works in negotiation research. Along the way, we offer illustrative examples as well as ideas for future research at the nexus of entrepreneurship and negotiation.

MODEL UNCERTAINTY AND FINANCIAL FRICTIONS: IMPLICATIONS FOR OPTIMAL MONETARY POLICY

The last decades proved that policymaking without considering uncertainty is impracticable. In an environment of uncertainty, policymakers have doubts about the policy models they routinely use. This paper focuses specifically on the situation where uncertainty on the financial side of the economy leads to misspecification in the policy model. We describe a coherent strategy for policymakers who are averse to model misspecification and analyze optimal policy design in the face of Knightian uncertainty. To do so, we augment a financial dynamic stochastic general equilibrium model with model misspecification in a simple minimax framework where the central bank plays a zero-sum game versus a hypothetical evil agent. The policy is tailored to insure against the worst-case outcomes. We show that model ambiguity on the financial side requires a passive monetary policy stance. However, if the uncertainty originates from the supply side of the economy, an aggressive response of interest rate is required. We also show the impact of an additional macroprudential tool on the dynamics of the economy.