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This is the first book to investigate individual’s pessimistic and optimistic prospects for the future and their economic consequences based on sound mathematical foundations. The book focuses on fundamental uncertainty called Knightian uncertainty, where the probability distribution governing uncertainty is unknown, and it provides the reader with methods to formulate how pessimism and optimism act in an economy in a strict and unified way. After presenting decision-theoretic foundations for prudent behaviors under Knightian uncertainty, the book applies these ideas to economic models that include portfolio inertia, indeterminacy of equilibria in the Arrow-Debreu economy and in a stochastic overlapping-generations economy, learning, dynamic asset-pricing models, search, real options, and liquidity preferences. The book then proceeds to characterizations of pessimistic (ε-fearful) and optimistic (ε-hopeful) behaviors under Knightian uncertainty and people’s inherent pessimism (surprise aversion) and optimism (surprise loving). Those characterizations are shown to be useful in understanding several observed behaviors in the global financial crisis and in its aftermath. The book is highly recommended not only to researchers who wish to understand the mechanism of how pessimism and optimism affect economic phenomena, but also to policy makers contemplating effective economic policies whose success delicately hinges upon people’s mindsets in the market.

Kiyohiko Nishimura is Professor at the National Graduate Institute for Policy Studies (GRIPS) and Professor Emeritus and Distinguished Project Research Fellow of the Center for Advanced Research in Finance at The University of Tokyo. Hiroyuki Ozaki is Professor of Economics at Keio University.



Chapter 1. Overall Introduction

This book is about “uncertainty” in decision science and economic science and its application to everyday problems we face.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 2. Mathematics for Reading Later Chapters

This chapter covers a number of mathematical concepts that are used in the following chapters.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 3. Decision-Theoretic Foundations of Knightian Uncertainty

This section surveys the decision-theoretic foundations of economic models with Knightian uncertainty. In later chapters, we often assume that the economic agents exhibit aversion to Knightian uncertainty in opportunities of decision-making. One of the main objectives of this chapter is to characterize the behaviors of such agents by some set of behavioral axiomsAxiom that are imposed directly on their primitive preferences over “acts.”

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 4. Portfolio Inertia

One of the most important implications of assuming an uncertainty-averse economic agent was presented by Dow and Werlang (Econometrica, 60:197–204, 1992). They considered an investor who does not hold any asset currently but who contemplates whether to take either a long or short position for some asset by anticipating any return from that asset in the future.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 5. Equilibrium Indeterminacy in Arrow–Debreu Economy with Knightian Uncertainty

This chapter describes the Arrow–Debreu economy with Knightian uncertainty as developed by Dana (Economic Theory, 23:569–587, 2004, Dana (2004)). We show that indeterminacy can arise in this economy, although it is very “rare” in the sense we make clear below.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 6. Monetary Equilibria and Knightian Uncertainty

In the past two decades, the implications of Knightian uncertainty have been explored in several general equilibrium settings. As shown by (Econometrica 60: 197–204 (1992)) Dow and Werlang (1992), (J Econ Dyn Control 22: 357–368 (1998)) Tallon (1998), (J Math Econ 61: 953–957 (2000)) Chateauneuf et al. (2000), and (Econ Theo 23: 569–587 (2004))Dana (2004), one of the most important findings in the existing literature is that indeterminacy of equilibria can be generated in the static Arrow-Debreu economy under Knightian uncertainty when there is no aggregate uncertainty.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 7. Dynamic Programming

Ozaki H, Streufert PA (1996). Dynamic programming for non-additive stochastic objectives. J Math Econ 25:391–442 (Ozaki and Streufert (1996)) and Ozaki H (2002). Dynamic programming with upper semi-continuous stochastic aggregator. Adv. Math. Econ 4:25–39 (Ozaki (2002)) developed a theory ofDynamic programming stochastic dynamic programming by generalizing the expectation operator E to a more abstract operator M, which maps a measurable function to another measurable function.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 8. Dynamic Asset Pricing

One of the main objectives of this chapter is to show that the indeterminacy of equilibria may show up in a truly dynamic framework. In this sense, this chapter is very closely related to Chaps. 4–6.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 9. Search and Knightian Uncertainty

Consider an unemployed worker who is searching for a job. Suppose that “uncertainty” about labor market conditions has increased. Does this change induce her to searchSearch longer and more intensively, or shorter and less intensively? The answer to this question has utmost importance both in macroeconomics concerning the aggregate unemployment rate and microeconomics explaining worker behavior.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 10. Irreversible Investment and Knightian Uncertainty

The investment decisions of any firm typically involve three features. First, future market conditions are uncertain. Second, the cost of investment cannot be retrieved and thus investment is irreversible. Third, the opportunity to invest does not vanish at once such that choosing a time to invest becomes a critical decision.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 11. Liquidity Preference and Knightian Uncertainty

Without doubt, moneyMoney is the most liquid asset. The conversion of money to other assets is immediate and costless, whereas the conversion of nonmoney assets to other assets including money involves time and substantial transaction costs. Thus, money enables prompt movement among various forms of investment, both financial and real. In a sense, money offers liquidity services.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 12. A Simple Characterization of Pessimism and Optimism: -Contamination Versus -Exuberance

On Wall Street, there are bulls and bears among professional investors. On Main Street, ordinary people are sometimes overly optimistic about their future and at other times excessively pessimistic. Bulls and bears on Wall Street often have starkly different views about the markets even though the available information is not so different among them. People on Main Street often switch from optimismOptimism to pessimismPessimism and vice versa quite easily even though there may not be noticeable change in their conditions.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 13. Persistent Pessimism and Optimism in Forecasts: Implicit Means and Law of Iterated Integrals

Economic activities have become increasingly complicated in recent years. For example, financial innovation, past and present, has increased the complexity of financial information. Securitization is one manifestation of this trend, and it generates an extraordinary degree of complexity.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 14. Learning Under Knightian Uncertainty

Economic agentsKnightian uncertaintylearning under Knightian uncertainty including policy makers face various uncertainties when they make decisions. Here we must distinguish between two different kinds of uncertainty. The first one, which is often called risk, is formulated as a known probability distribution with possibly unknown parameters that can be learned from past experience of, say, stock prices and the GDP growth rate in the near future.

Kiyohiko G. Nishimura, Hiroyuki Ozaki

Chapter 15. Areas of Further Research

This chapter briefly reviews further and ongoing research along the lines developed in this book.

Kiyohiko G. Nishimura, Hiroyuki Ozaki


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