Graciela Chichilnisky

Modtiiing with Scenarios 303 MODELLING WITH SCENARIOS Technology in North-South development Sara Cole and Graciela Cbichilnisky This article outlines work in progress on a study of technological choice in the context of North-South development Its main purpose is to describe the ...

It has been said that insurance is the last of the financial services to accept radical change (Denney [1995-1996]). Yet there has been a fundamental shift in the geographic location and in the organization of the reinsurance industry in the last six years (Chichilnisky [19966]). Global environmental risks are partly responsible for this change; increased weather volatility and catastrophic risks are difficult to diversify using traditional insurance practices. To provide a map to the future, we need a realistic appraisal of how we got where we are. This is the story of how humans have hedged risks. There are two basic and distinct approaches: statistical and economic. The former is typical of the insurance industry; the latter typifies the securities industry. Both are needed to manage today's catastrophic risks. Neither alone will do. We show how a combination of both leads to efficient outcomes, and is the way to the future (Chichilnisky [1996a, 1996b, 1996d]).

Abstract We extend the foundation of subjective probability to integrate rare events that are potentially catastrophic, called black swans, such as nat- ural hazards, market crashes, catastrophic climate change and major episodes of species extinction. Such events are generally treated as ...

We extend Bergstrom's 1985 results on nonparametric (NP) estimation in Hilbert spaces to unbounded sample sets. The motivation is to seek the most general possible framework for econometrics, NP estimation with no a priori assumptions on the functional relations nor on the observed data. In seeking the boundaries of the possible, however, we run against a sharp dividing line, which defines a necessary and sufficient condition for NP estimation. We identify this condition somewhat surprisingly with a classic statistical assumption on the relative likelihood of bounded and unbounded events (DeGroot, 2004). Other equivalent conditions are found in other fields: decision theory and choice under uncertainty (monotone continuity axiom (Arrow, 1970), insensitivity to rare events (Chichilnisky, 2000), and dynamic growth models (dictatorship of the present; Chichilnisky, 1996). When the crucial condition works, NP estimation can be extended to the sample space R +. Otherwise the estimators, which are based on Fourier coefficients, do not converge: the underlying distributions are shown to have " heavy tails " and to contain purely finitely additive measures. Purely finitely additive measures are not constructible, and their existence has been shown to be equivalent to the axiom of choice in mathematics. Statistics and econometrics involving purely finitely additive measures are still open issues, which suggests the current limits of econometrics.

Aggressive efficiency improvements and a shift away from fossil fuels cannot offset climate change threats. This realization creates an imperative for ‘carbon-negative’ mitigation measures; that is, measures that can reduce atmospheric carbon faster than emissions will load the atmosphere. Among such measures, air extraction technology, coupled with secure sequestration, offers advantages of centralization and control without direct intervention in the biosphere or major collateral environmental impact. Significant new scientific developments in air extraction show promise of greatly reduced costs, such that decreasing the concentration of carbon in the atmosphere to substantailly lower risk levels may be economically practicable. These developments create a strong case for expanded R&D efforts aimed at advancing air extraction technology.

This article studies decisions made under conditions of fear, when a catastrophic out- come is introduced in a lottery. It reports on experimental results and seeks to compare the predictions of the expected utility (EU) framework with those of a new axiomatic treatment of choice under uncertainty that takes explicit account of emotions such as fear (Chichilnisky, 1996, 2000, 2002). Results provide evidence that fear influences the cognitive process of decision-making by leading some subjects to focus excessively on catastrophic events. Such heterogeneity in subjects’ behavior, while not consistent with EU-based func- tions, is fully consistent with the new type of utility function implied by the new axioms.

For many years experimental observations have raised questions about the rationality of economic agents—for example, the Allais Paradox or the Equity Premium Puzzle. The prob- lem is a narrow notion of rationality that disregards fear. This article extends the notion of rationality with new axioms of choice under uncertainty and the decision criteria they imply (Chichilnisky, G., 1996a. An axiomatic approach to sustainable development. Social Choice andWelfare 13, 257–321; Chichilnisky, G., 2000. An axiomatic approach to choice under uncertainty with Catastrophic risks. Resource and Energy Economics; Chichilnisky, G., 2002. Catastrophical Risk. Encyclopedia of Environmetrics, vol. 1. John Wiley & Sons, Ltd., Chicester). In the absence of catastrophes, the old and the new approach coincide, and both lead to standard expected utility. A sharp difference emerges when facing rare events with important consequences, or catastrophes. Theorem 1 establishes that a classic axiom of choice under uncertainty – Arrow’s Monotone Continuity axiom, or its relatives introduced by DeGroot, Villegas, Hernstein and Milnor – postulate rational behavior that is ‘insensitive’ to rare events as defined in (Chichilnisky, G., 1996a. An axiomatic approach to sustainable development. Social Choice andWelfare 13, 257–321; Chichilnisky, G., 2000. An axiomatic approach to choice under uncertainty with Catastrophic risks. Resource and Energy Eco- nomics; Chichilnisky, G., 2002. Catastrophical Risk. Encyclopedia of Environmetrics, vol. 1. John Wiley & Sons, Ltd., Chicester). Theorem 2 replaces this axiom with another that allows extreme responses to extreme events, and characterizes the implied decision criteria as a combination of expected utility with extremal responses. Theorems 1 and 2 offer a new understanding of rationality consistent with previously unexplained observations about decisions involving rare and catastrophic events, decisions involving fear, the Equity Pre- mium Puzzle, ‘jump diffusion’ processes and ‘heavy tails’, and it agrees with (Debreu, G., 1953. Valuation equilibrium and Pareto optimum. Proceedings of the National Academy of Sciences, 40, 588–592) formulation of market behavior and his proof of Adam Smith’s Invisible Hand theorem.

We extend the foundation of statistics to integrate rare events that are potentially catastrophic, called black swans.These include natural hazards, regime change in complex systems, market crashes, catastrophic climate change and major episodes of species extinction. Classic statistics and physics treat such events as 'outliers' and often disregard them. We propose a new axiomatization of subjective probability requiring equal treatment for rare and frequent events, and characterize the likelihoods or subjective probabilities that the axioms imply. These coincide with countably additive measures and yield normal distributions when the sample has no black swans. When the sample includes black swans, the new likelihoods are represented by a combination of countable and finitely additive measures with both parts present. The axioms were introduced in Chichilnisky (2000, 2002); they extend the axiomatic foundations of Savage (1954), Villegas (1964) and Arrow (1971) and they are valid for bounded and unbounded samples (Chichilnisky, 1996b). The finitely additive measures assign more weight to rare events than do standard distributions and in that sense explain the persistent observation of power laws and 'heavy tails' that eludes classic theory.

Equal treatment for the present and the future was required in two axioms introduced in the articles by Chichilnisky of the years 1996 and 1997. These articles provide a characterization of the decision criterion that satisfies the axioms and shows that the two axioms are equivalent to physical limits in the long-run future. The author proves that maximizing discounted utility with a long-run survival constraint is equivalent to maximizing a criterion that treats equally the present and the future. The equal treatment axioms are therefore the essence of sustainable development. The " weight " λ given to the long-run future is here identified with the marginal utility of the environmental asset along a path that narrowly misses extinction. An existence theorem is also provided for optimizing according to the welfare criterion that treats equally the present and the future. The author shows that no prior welfare criteria satisfy the axioms for sustainable development introduced in her article of the year 1996.

We extend Bergstrom's 1985 results on nonparametric (NP) estimation in Hilbert spaces to unbounded sample sets. The motivation is to seek the most general possible framework for econometrics, NP estimation with no a priori assumptions on the functional relations nor on the observed data. In seeking the boundaries of the possible, however, we run against a sharp dividing line, which defines a necessary and sufficient condition for NP estimation. We identify this condition somewhat surprisingly with a classic statistical assumption on the relative likelihood of bounded and unbounded events (DeGroot, 2004). Other equivalent conditions are found in other fields: decision theory and choice under uncertainty (monotone continuity axiom (Arrow, 1970), insensitivity to rare events (Chichilnisky, 2000), and dynamic growth models (dictatorship of the present; Chichilnisky, 1996). When the crucial condition works, NP estimation can be extended to the sample space R +. Otherwise the estimators, which are based on Fourier coefficients, do not converge: the underlying distributions are shown to have " heavy tails " and to contain purely finitely additive measures. Purely finitely additive measures are not constructible, and their existence has been shown to be equivalent to the axiom of choice in mathematics. Statistics and econometrics involving purely finitely additive measures are still open issues, which suggests the current limits of econometrics.

We study the introduction of new assets that are defined in expected values rather than state by state. Individual default emerges naturally in an economy where such assets are introduced without completing all contingency markets. We further provide conditions under which individual default is propagated endoge-nously into a collective risk of widespread default in general equilibrium. We prove existence of a general equilibrium with endogenous uncertainty.

This paper analyses decision under uncertainty with catastrophic risks, and is motivated by problems emerging from global environmental risks. These are typically low-probability events with major irreversible consequences. For such risks, the Von Neumann-Morgens-tern (NM) axioms for decision making under uncertainty are not appropriate, since they are shown here to be insensitive to low-probability events. The paper introduces an alternative set of axioms requiring sensitivity to both low-and large-probability events. Through a new representation theorem in functional analysis, the results characterize all the operators whose maximization leads to the fulfillment of these axioms. They involve a convex combination of expected utility and a criterion based on the desire to avoid low probability and potentially catastrophic events. It is shown that the new axioms help resolve the Allais paradox. Open questions about risk aversion, games under uncertainty and calculus of variations are discussed .

The paper proposes two axioms that capture the idea of sustainable development and derives the welfare criterion that they imply.The axioms require that neither the present nor the future should play a dictatorial role.
Theorem 1shows there exist sustainable preferences, which satisfy these axioms. They exhibit sensitivity to the present and to the long-run future, and specify trade-offs between them . It examines other welfare criteria which are generally utilized: discounted utility, lim inf. long run averages, overtaking and catching-up criteria, Ramsey's criterion, Rawlsian rules, and the criterion of satisfaction of basic needs, and finds that none satisfies the axioms for sustainability.
Theorem 2 gives a characterization of all continuous independent sustainable preferences.Theorem 3 shows that in general sustainable growth paths cannot be approximated by paths which approximate discounted optima. Proposition 1 shows that paths which maximize the present value under a standard price system may fail to reach optimal sustainable welfare levels, and Example 4 that the two criteria can give rise to different value systems.

This paper examines how, in the presence of individual risk, economic efficiency can be achieved without an unrealistically large number of contingent claims. Market uncertainty is specified in such a way that general types of individual risk and collective risk are properly accounted for and so that, specifically, market clearing is always satisfied ex post as well as ex ante. We show that consistency of beliefs and optimality of allocation can be guaranteed with an appropriate array of pure Arrow securities to spread collective risk and mutual insurance policies to pool individual risk. When there is individual risk common to like groups of individuals, pooling risk by means of mutual insurance permits substantial economizing on market transactions, as compared to those required if dealing instead with the full complement of pure Arrow securities. We show that if there are N households (consisting of H types), each facing the possibility of being in S individual states together with T collective states, then ensuring Pareto optimality requires only H(S-1)T independent mutual insurance policies plus T pure Arrow securities. Our results also help to clarify the question of which missing markets may affect allocational efficiency .

We consider contracts to purchase assets by means of streams of payments over time, with the asset as security. These give the purchaser an option not present if all payment is made up fron, the option  of stopping payments and delivering the asset in satisfaction of the remaining debt. We argue that the value inherent in such options explains the attractions of asset-backed loans, employee stock options plan and MBOs.

Global environmental phenomena like climate change, major extinction events or flutype pandemics can have catastrophic consequences. By properly assessing the outcomes involved – especially those concerning human life – economic theory of choice under uncertainty is expected to help people take the best decision. However, the widely used expected utility theory values life in terms of the low probability of death someone would be willing to accept in order to receive extra payment. Common sense and experimental evidence refute this way of valuing life, and here we provide experimental evidence of people's unwillingness to accept a low probability of death, contrary to expected utility predictions. This work uses new axioms of choice, especially an axiom that allows extreme responses to extreme events, and the choice criterion that they imply. The implied decision criteria are a combination of expected utility with extreme responses, and seem more consistent with observations.