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In "Bargaining to Lose: The Permeability Approach to Post Transition Resource Extraction" [1] Natasha Chichilnisky-Heal introduces an original and fertile explanation for the resource curse. Her "permeability" approach questions the treatment of the state as a decision maker having the public good as an objective, and replaces it by the results of a bargaining game between the state and International organizations. Her new theory is illustrated with unique hands-on experience in the case of copper and gold mines in Mongolia and Zambia, and focuses on a bargaining game between the state and key financial organizations: the Bretton Woods Institutions (IMF, World Bank) and MNCs. This piece extends and generalizes "Bargaining to lose" providing economic models that validate the original conclusions, and exploring its implications for the global commons: the atmosphere, the oceans and biodiversity. Chichilnisky-Heal’s "permeable state" is a transition to a new globalized society where the sovereign state - a relatively recent creation - is receding giving rise to a new set of global economic agents and institutions that better explain the dynamics of the global commons. We show that the permeable state complements other explanations for the resource curse [2] as a global market failure magnified by globalization and based on the lack of well-defined property rights on natural resources during the pre-industrial period. We generalize Chichilnisky-Heal’s "bargaining to lose" approach to the resource curse and explore its natural implications for the environmental crisis on the global commons. The solutions that Chichilnisky-Heal proposes, e.g. limiting the Bretton Woods’ Institutions’ ‘seat at the negotiation table’ of resource extraction contracts, could help resolve the environmental crisis that is based on over-extraction of global resources.

Ramsey famously condemned discounting “future enjoyments” as “ethically indefensible”. Suppes enunciated an equity criterion which, when social choice is utilitarian, implies giving equal weight to all individuals’ utilities. By contrast, Arrow (Contemporary economic issues. International Economic Association Series. Palgrave Macmillan, London, 1999a; Discounting and Intergenerational Effects, Resources for the Future Press, Washington DC, 1999b) accepted, perhaps reluctantly, what he called Koopmans’ (Econometrica 28(2):287–309, 1960) “strong argument” implying that no equitable preference ordering exists for a sufficiently unrestricted domain of infinite utility streams. Here we derive an equitable utilitarian objective for a finite population based on a version of the Vickrey–Harsanyi original position, where there is an equal probability of becoming each person. For a potentially infinite population facing an exogenous stochastic process of extinction, an equitableextinction biasedoriginal position requires equalconditionalprobabilities, given that the individual’s generation survives the extinction process. Such a position is well-defined if and only if survival probabilities decline fast enough for the expected total number of individuals who can ever live to be finite. Then, provided that each individual’s utility is bounded both above and below, maximizing expected “extinction discounted” total utility—as advocated,inter alia, by theStern Reviewon climate change—provides a coherent and dynamically consistent equitable objective, even when the population size of each generation can be chosen.

Modern economic theory came to life in the middle of the twentieth century, providing the intellectual foundations for an unprecedented period of industrial expansion and globalization since World War II. Coupled with population growth, the successful trajectory of industrial society in the twentieth century led to a voracious use of natural resources and global environmental concerns in the twenty-first century. It is uncontested that, for the first time in recorded history, humans dominate the planet. We are changing the planet’s atmosphere, its bodies of water, and the complex web of species that makes life on earth. This radical change in circumstances led to rethinking of the foundations of human organization and, in particular, the industrial economy and the economic theory behind it. The rethinking is underway. Sustainable economics emerged in 1992 at the UN Earth Summit in Rio de Janeiro, anchored in the concept of BasicNeeds that was voted by 150 nations as a cornerstone of efforts to redefine economic development1. The formal theory of sustainable development was introduced in Chichilnisky (1997, 2000). In essence sustainable development seeks to meet the basic needs of the present without depriving the future from meeting its basic needs.

Market objectives can conflict with long-term goals. Behind the conflict is the impatience axiom introduced by T. Koopmans to describe choices over time. The conflict is resolved here by introducing a new concept, sustainable markets. These differ from Arrow-Debreu markets in that traders have sustainable preferences and no bounds on short sales. Sustainable preferences are sensitive to the basic needs of the present without sacrificing the needs of future generations and embody the essence of sustainable development (Chichilnisky 1996a, b). Theorems 1 and 2 show that limited arbitrage is a necessary and sufficient condition describing diversity and ensuring the existence of a sustainable market equilibrium where the invisible hand delivers sustainable as well as efficient solutions (Chichilnisky 1991, 1995; Chichilnisky and Heal 1998). In sustainable markets prices have a new role: they reflect both the value of instantaneous consumption and the value of the long-run future. The latter are suitably ambiguous, they are connected to the independence of the axiom of choice at the foundations of mathematics (Godel 1940).

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 substantially lower risk levels may be economically practicable. These developments create a strong case for expanded R&D efforts aimed at advancing air extraction technology.

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 endogenously into a collective risk of widespread default in general equilibrium. We prove existence of a general equilibrium with endogenous uncertainty. © 2006 Elsevier B.V. All rights reserved.

Classic probability theory treats rare events as ‘outliers’ that are disregarded and underestimated. In a moment of change however rare events can become frequent, and frequent events rare. We postulate new axioms for probability theory that require a balanced treatment of rare and frequent events, based on what we call “the topology of change”. The axioms extend the foundation of probability to integrate rare but potentially catastrophic events or black swans: natural hazards, market crashes, catastrophic climate change and episodes of species extinction. The new results include a characterization of a family of purely finitely additive measures that are—somewhat surprisingly—absolutely continuous with respect to the Lebesgue measure. This is a new development from an earlier characterization of probability measures implied by the new axioms, which where countably additive measures created in Chichilnisky (2000), Wiley, Chichester (2002), Chichilnisky (2009, 2009a). The results are contrasted to the axioms of Kolmogorov (1933/1950), De Groot (1970/2004), Arrow (1971), Dubins and Savage (1965), Savage (1972), Von Neumann and Morgernstern (1944), and Hernstein and Milnor.

A single condition, limited arbitrage, is shown to be necessary and sufficient for the existence of a competitive equilibrium and the core in economies with any number of markets, finite or infinite, with or without short sales. This extends earlier results of Chichilnisky [8] for finite economies. This unification of finite and infinite economies is achieved by proving that in Hilbert spaces limited arbitrage is necessary and sufficient for the compactness of the Pareto frontier. Limited arbitrage has also been shown to be necessary and sufficient for a resolution of the social choice paradox [9], [10], [12], [13], [14].

Classic formulations of markets regard uncertainty as originating from acts of nature. l extend this to a formulation of markets which face risks induced by the economy itself, such as the environmental risks of atmospheric and climate change induced by CFC and CO; emissions. l formulate and prove the existence of a general competitive equilibrium where the state space and the probabilities of events are endogenously determined as part of the equilibrium. Traders take optimal positions with respect to the uncertainty which their own actions induce. The equilibrium allocations are efficient in a restricted sense. l show that scientific uncertainty can be fully hedged. However uncertainty induced by the unknown level of output at an equilibrium cannot be hedged fully. l discuss applications for CAT Futures. recently introduced on the Chicago Board of Trade, and to international environmental strategies.

A close connection is drawn between the non-emptiness of the core and limited arbitrage, a condition originally defined on the preferences and endowments of the traders of an Arrow-Debreu economy in Chichilnisky (1992, 1993b, 1994, 1995a,b). This condition limits the traders' diversity, and bounds their mutually beneficial gains from trade.

This paper studies maps which are invariant under the action of the symmetry group S k . The problem originates in social choice theory: there are k individuals each with a space of preferences X, and a social choice map ϕ:X k → X which is anonymous i.e. invariant under the action of a group of symmetries. Theorem 1 proves that a full range map ψ:X k → X exists which is invariant under the action of S k only if, for all i≥1, the elements of the homotopy group Π i (X) have orders relatively prime with k. Theorem 2 derives a similar results for actions of subgroups of the group S k . Theorem 3 proves necessary and sufficient condition for a parafinite CW complex X to admit full range invariant maps for any prime number k:X must be contractible.

The theory of social choice introduced in [5,6] is robust; it is completely independent of the choice of topology on spaces of preference. This theory has been fruitful in linking diverse forms of resource allocation; it has been shown [17] that contractibility is necessary and sufficient for solving the social choice paradox; this condition is equivalent [11] to another- limited arbitrage- which is necessary and sufficient for the existence of a competitive equilibrium and the core of an economy [13, 14, 15, 16, 17]. The space of monotone preferences is contractible; as shown already in [6, 17] such that spaces admit social choice rules. However, monotone preferences are of little interest in social choice theory becasue the essence of the social choice problem, such as Condorcet triples, rules out monotonicity.

Chaotic behavior of prices can emerge as a robust result from a very simple and standard price adjustment process. Consider the dynamics of prices adjusting according to supply and demand in economies with increasing returns to scale. Increasing returns in production implies the existence of a globally attracting set of prices, containing a stable disequilibrium price, within which the motion of the system is chaotic. This property holds for any step size in the price adjustment process when consumption and leisure are complementary. We prove that long-run statistical properties of the system's behavior in this set are described by an ergodic measure. Price dynamics drive the system into the globally attracting region, and then chaotic motion takes over. On average according to this measure there is excess supply. We suggest possible empirical implications of our analysis, particularly with respect to the relationship between wages changes and the demand for labor, the “Phillips curve”.

We prove the existence of an optimal growth path in an economy where goods that are not consumed are either invested in next period capital or in R&D with overall non-convex production possibilities, using results of non-linear functional analysis in weighted Lp spaces of Chichilnisky (Journal of Optimization Theory and Applications, 1977, 61, no. 2, 504–520) and (Journal of Mathematical Economics, 1981, 8, 1–14).

A condition oflimited arbitrage is defined on the endowments and the preferences of the traders in an Arrow-Debreu economy. Theorem 1 establishes thatlimited arbitrage is necessary and sufficient for the existence of a competitive equilibrium in markets with or without short sales. Limited arbitrage bounds utility arbitrages, the diversity of the traders in the economy, and the gains from trade which they can afford from initial endowments (Proposition 2); it is related to but nonetheless different from the no-arbitrage condition used in finance. Theorem 2 establishes that an Arrow — Debreu economy has a competitive equilibrium if and only if every one of its subeconomies withN + 1 traders does, whereN is the number of commodities. Limited arbitrage has been shown elsewhere to be equivalent to the existence of the core [16], to the contractibility of spaces of preferences and to the existence of continuous anonymous social choice rules which respect unanimity [10], [14], [15], [16].

Summary We use growth models with natural resources to study the consequences of a ranking of intertemporal paths, due to Chichilnisky, which places weight on their very long run or limiting characteristics as well as on their characteristics over any finite period. This criterion shows more intertemporal symmetry or egalitarianism than the discounted utilitarian approach, which clearly emphasizes the immediate future at the expense of the long run. In this respect it captures the concenrs of those who argue for sustainability and for a heightened sense of responsibility to the future. In some of the examples that we consider, the long-run characteristics of paths optimal by this criterion are a mixture of those of utilitarian paths and the “green golden rule” (the configuration which maximizes long-run sustainable utility from consumption and environment).

We review the optimal pattern of carbon emission abatements across countries in a simple multi-country world. We model explicitly (with the model in Chichilnisky [4]) the fact that the atmosphere is a public good. Within this framework we establish conditions for it to be necessary for optimality that the marginal cost of abatement be the same in all countries. These condition are quite restrictive, and amount to either ignoring distributional issues between countries or operating within a framework within which lump-sum transfers can be made between countries. These results have implications for the use of tradeable emission permits, which as normally advocated will lead to the equalization of marginal abatement costs across countries. The observation that the atmosphere is a public good implies that we may need to look at a Lindahl equilibrium rather than a Walrasian equilibrium in tradeable permits.

ACL-1; International audience; 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 defined by Chichilnisky (2000), 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.

This chapter presents an application of competitive general equilibrium theory of markets in the spirit of Walras, formalized in the 1950s by K. Arrow and by G. Debreu. In using general equilibrium theory to generate insight into current policy issues, it follows a tradition established by Arrow in his work on welfare economics of medical care (1963), on the organization of economic activity (1969), on the evaluation of public investment (Arrow and Lind, 1970), and in urban development (1970). The intention if to use formalized general equilibrium theory to derive general statements about the economic behavior and interrelations between two groups of countries: industrial and developing countries.The goal is to obtain simple and general results, and for this purpose we consider a styled model with the minimum of characteristics needed for the task: two regions, two produced goods, and two factors of production. Within this simple model, we explore issues of current import, such as export-led policies and the transmission of economic activity between regions.

This paper studies a general equilibrium North-South economy consisting of two countries which produce and trade two goods using two inputs of production. It extends the North-South trade model of Chichilnisky (1981, 1986) by assuming that one input of production is a renewable resource which follows its own physical dynamics. From these dynamics and from optimal extraction behavior we derive explicitly the supply of environmental inputs as a function of their market prices. Therefore this paper fully derives the price dependence of inputs which is postulated exogenously in the original North-South model. All markets for goods and for inputs are free and competitive throughout. We establish that different property regimes lead to different supply functions for environmental resources. When property rights are well defined (as in the North) the supply of environmental inputs is less price responsive than it is when property rights are ill defined (as in the South). Ill defined property rights lead to an apparent ‘abundance’ of environmental resources in the south. We establish that the difference in property rights in two otherwise identical regions (the same technologies, preferences, and endowments) is itself sufficient to explain why the two regions trade. The region with ill defined property rights exports the environmentally intensive good. This leads to overuse of the environment worldwide and to lower market prices of environmentally intensive goods. The difference in property rights of the two regions determines an apparent ‘comparative advantage’ in the export of environmentally intensive goods in the South, even when the two countries are identical and therefore there is no real comparative advantages. The difference in property rights also gives rise to ‘apparent’ gains from trade, even when there are no real gains from trade.

Following Chichilnisky and Chichilnisky-Kalman we establish existence and optimality of competitive equilibrium when commodity spaces are infinite dimensional Sobolov spaces, including Hilbert spaces such as weighted L2 which have L∞, as dense subspaces. We allow general consumption sets with or without lower bounds, thus including securities markets with infinitely many assets and unbounded short sales, and economies with production. We give non-arbitrage conditions on endowments and preferences which suffice for the existence of an equilibrium. Prices are in the same space as commodities. Equilibrium allocations are approximated by allocations in other frequently used spaces such as C(R) and L∞.

This note links two conditions which have generated some interest in the literature and have an important role in proving the existence of an equilibrium, the second welfare theorem and the core equivalence theorem in infinite dimensional commodity spaces: These are thecone condition introduced in Chichilnisky and Kaiman (1980), and theproperness condition in Mas-Colell (1986a), which were studied also in Yannelis and Zame (1986), Aliprantis et al. (1987a, b) and (1989), Aliprantis and Burkinshaw (1988), Mas-Colell (1986b), Chichilnisky and Heal (1984, 1992), and Rustichini and Yannelis (1991) among others. I establish that these two conditions are the same. Indeed, the cone condition coincides also with the assumption of anextremely desirable commodity used in Yannelis and Zame (1986) and Rustichini and Yannelis (1991). The motivation for studying these conditions comes from the same economic application, showing the need to bring within the scope of equilibrium theory commodity spaces whose positive orthants have empty interior, a typical situation in infinite dimensional linear spaces.

The purpose of this note is to clarify and complement several comments on my work [Chichilnisky, 1980, 1982a], which appeared in this Journal: Baigent [1987], Nitzan [1989], and Baigent [1989]. I shall offer two new results. The first result constructs a continuous, anonymous social selection rule that respects unanimity and the proximity of preferences, for a large family of preferences (Theorem 1). This complements the result of Nitzan [1989] and Baigent's [1989] extension of it and is achieved by accepting, as they do, that social outcomes be optimal choices, rather than rankings of all possible choices or social preferences This result is of interest because it appears to contradict the original impossibility theorem of Chichilnisky, which establishes that, for the same family of preferences, social aggregation rules with these properties do not exist (Theorem 2).

We consider the economics of global environmental risks. In this area, we are dealing with risks that are poorly understood, endogenous, collective, and irreversible. In policy terms, the nature and extent of uncertainty about global climate change implies that society's position will be dominated by two questions: What cost is worth incurring to reduce the poorly-understood risk of climate change, or to improve our understanding of the risk? How may existing social institutions, such as insurance contracts and securities markets, be used to provide the most efficient allocation of the risks associated with global climate change?

We evaluate two risk profiles: (i) global warming risks and (ii) collisions with asteroids that can cause the extinction of our species. The expected values computed for these two risks suggest that no action will be taken to avoid extinction. The result is somewhat counterintuitive, but it is typical of the results of using classic decision theory to evaluate catastrophic risks in the distant future, see the study by Posner (2004). We establish why expected value is insensitive to catastrophic risks see the study by Chichilnisky (1996), and use another criterion to evaluate risk based on axioms for choice under uncertainty that update the classic Von Neumann theory and require equal treatment for rare and frequent events. Optimizing according to the new criterion is shown to be equivalent to optimizing expected utility with a restriction on the worst outcome in the case of a catastrophe. The evaluation obtained from the new criterion seems more intuitively plausible, and suggests a more practical and realistic approach to catastrophic risks: optimizing expected value while minimizing losses in the case of a catastrophe.

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 anecessary and sufficient conditionfor 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 spaceR+. 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.

« Aucune machine, aucun algorithme, ne pourra jamais être construit pour remplacer les valeurs et les décisions humaines. »

This paper develops a theory of the gender wage gap. In a general equilib- rium model, spouses devide their labor between a formal sector and a home sector. Due to indivisibility eects, productivity of labor in the formal sector is negatively related to labor used in the home; at the same time labor inputs are complementary in home production. We show that initial beliefs about the gender wage gap are self-ful…lling, and a central result is multiplicity of equilibria. Spouses allocate their labor equally, if they expect to earn the same wage rates, which ex post reinforces equal wage rates; whereas they allocate their labor dierently, if they expect to earn dierent wage rates. The latter situation manifests itself in a gender wage gap. By use of numer- ical examples, we show that welfare is highest when spouses allocate labor equally. We relate this …nding to policy recommendations.

For any intransitive community preference, we construct a non-convex economy where all the marginal cost pricing general equilibria are Pareto inefficient (theorem 3.2). The result is valid without requiring a fixed income distribution rule (corollary 3.3). Intransitive community preferences are a frequent occurrence (theorem 3.1): necessary and sufficient conditions for transitivity of the community preference fail in a set which is open and dense in the space of individual preferences with a standard topology.

Sectors with increasing returns to scale have been shown to amplify business cycles exhibiting more volatility than others [13]. Our hypothesis is that this volatility could be a cause of the “jobless recovery” suggesting policies for employment generation. To test this hypothesis we introduce a general equilibrium model with involuntary unemployment. The economy has two sectors: one with increasing returns that are external to the firm and endogenously determined — the knowledge sector — and the other with constant returns to scale. We define a measure of employment volatility, a ‘labor beta’ that is a relative of the ‘beta’ used in finance. A ‘resolving’ equation is derived from which it is proved that increasing return sectors exhibit more employment volatility then other sectors. The theoretical results are validated on US macro economic data of employment by industry (2–3 digits SIC codes) of the 1947–2001 period, showing that the highest ‘labor betas’ are in the service sectors with increasing returns to scale. Policy conclusions are provided to solve the puzzle of the ‘jobless recovery’, where small firms in the services industry play a key role. We conclude with policy recommendations on how to create jobs in the knowledge economy.

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 endogenously into a collective risk of widespread default in general equilibrium. We prove existence of a general equilibrium with endogenous uncertainty.

Summary. We seek to explain the economic volatility of the last 6 years, in particular the rapid expansion and contraction of the knowledge sectors. Our hypothesis is that these sectors amplify the business cycle due to their increasing returns to scale, growing faster than others in an upswing and contracting faster in a downswing. To test this hypothesis we postulate a general equilibrium model with two sectors: one with increasing returns that are external to the firm and endogenously determined – the knowledge sector – and the other with constant returns to scale. We introduce a new measure of volatility of output, a ‘real beta’, and derive a ‘resolving’ equation, from which we prove that the increasing return sectors exhibit more volatility then other sectors. We validate the main results on US macro economic data of real GDP by industry (2-3 digits SIC codes) of the 1977–2001 period, and provide policy conclusions.

CurrentchangesinLatinAmerica includetheabandonment oftheeconomic pattern ofimportsubstitution, a growing opening ofthe nationaleconomies,a continental wave ofpoliticaldemocratization,an apparent economic recoveryfrom the "lost decade" (the1980s),a growing socialpolarization, a worsening ofenvironmental problems,the growing influenceofthe market,and the most intenseurbanization processon the planet.The aim ofthispaper isnot todiscussthe advantages or disadvantagesof the prevailingeconomic pattern,but only to analyze some of thepossibleenvironmental implicationsderived from the way of insertionofthe countriesofthe regioninthe globaleconomy .The regionasa whole isrelatively wellendowed interms ofnaturalresources.With littlemore than 8% ofthe globalpopulation,Latin America has 23% ofthe potentiallyarableland,10% ofthe !-' cultivatedland,17% ofthe pastures,22% ofthe forests(and 52% ofthe tropical `:forests), and 31% ofthe permanently usablefreshwater.Ithas not lessthan 3% of the world reservesoffossilfueland 19% of the technicallyusable hydroelectric rPower.

Two major trends in the world economy are international migration and environmental degradation. The object of the paper is to analyze the connection between these two trends, which have generally been analyzed in isolation. Here we represent a world economy in which the exploitation of natural resources as well as the migration of labor have a global character. We discuss the welfare impact of migration and exploitation of natural resources. and policies to address these issues.

The present acceleration of environmental destruction can be linked to the economic trading strategies that came into vogue after World War II. The theory of comparative advantages of trade, which recommends that developing countries emphasize resource exports and exports of labor-intensive products, has proven devastating to both the economies and environments of Latin America and Africa. In contrast, the Asian Tigers approach based on external economies of scale, has generated knowledge-intensive products where benefits spread across whole industries and whole economies, leading to more economic growth with much less environmental degradation. Such an approach should be promoted throughout the world trading system instead of the resource-intensive patterns of growth that continue to threaten our global environment. This is particularly important because other resource-conserving strategies, such as green accounting and property rights regimes, remain politically unattainable.

The need to manage climate risks is not a new: it has shaped social institutions for many centuries. In medieval England, a peasant farmer’s land was broken into many widely-dispersed parcels. Economic historians interpret this as a way of hedging climate risk (see references in Bromley [9]). Land in different locations would be affected differently by droughts, floods and frosts. By spreading land holdings over different locations, as well as by organizing agricultural cooperatives and buying insurance, farmers have managed climate risk for many centuries.

New risks seem to be an unavoidable in a period of rapid change. The last few decades have brought us the risks of global warming, nuclear meltdown, ozone depletion, failure of satellite launcher rockets, collision of supertankers, AIDS and Ebola.l A key feature of a new risk, as opposed to an old and familiar one, is that one knows little about it. In particular, one knows little about the chances or the costs of its occurrence. This makes it hard to manage these risks: existing paradigms for the rational management of risks require that we associate probabilities to various levels of losses. This poses particular challenges for the insurance industry, which is at the leading edge of risk management. Misestimation of new risks has lead to several bankruptcies in the insurance and reinsurance businesses.2 In this paper we propose a novel framework for providing insurance cover against risks whose parameters are unknown. In fact many of the risks at issue may be not just unknown but also unknowable: it is difficult to imagine repetition of the events leading to global warming or ozone depletion, and, therefore, difficult to devise a relative frequency associated with repeated experiments.

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 [1996b]). Global environmental risks are partly responsible For this change; increased weather volatility and catastrophic risks are difficult to diversify using traditional insurance practices.

An important problem in environmental economics arises from the irreversibility of consuming or destroying certain resources. Extractive resources like oil are a clear example. Even for environmental resources the same seems to be true in a number of important cases, for example biodiversity, current climate conditions, or complex ecological systems. Irreversibility imposes a severe externality across different generations; future generations will suffer from the destruction of a unique asset like Amazonia, and it is not clear how such a loss could be compensated in terms of other goods. If such an asset is destroyed, then it is not possible subsequently to restore it. In contrast, if the asset is preserved, then it is possible to “use” the asset at a subsequent date. If there is uncertainty about future preferences or valuations, then preservation provides a type of insurance which is not available if the irreversible decision is carried out.

Complexity theory is designed to bring order out of a rough-and- tumble world, something close to every insurance professional's or actuary's heart. Whether applied in the laboratory or as part of a mathematical model, it can do wonderful things . But in the real world it's just what its name says-a theory. It may help us understand why things go one way or another, but it can't foretell those things with such certainty that an insurance company could, say, set its rates based on the knowledge that only one hurricane will strike Florida during the coming year...