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1 The Economics of the Global Environment-Catastrophic Risks in Theory and Practice; 1 Introduction; 2 Part I. Catastrophic Risk in Economic Theory; 3 Part II. Ethical and Welfare Considerations; 4 Part III. The Environment in a Global Context; 5 Part IV. The Case of Climate Change; 6 Part V. Economic Policy and Regulation; 7 Part VI. Catastrophic Risk in Economic Practice; References; Part I Catastrophic Risk in Economic Theory; Catastrophic Risk, Rare Events, and Black Swans: Could There Be a Countably Additive Synthesis?; 1 Introduction.
1.1 Countably Additive Subjective Probability1.2 Monotonicity; 1.3 Beyond Monotonicity; 1.4 Outline of Paper; 2 Catastrophic Risk; 2.1 Etymology; 2.2 Catastrophic Consequences; 2.3 Assumptions; 2.4 Money Metric Utility; 2.5 A Critical Probability Level: Catastrophic Risk; 2.6 Extreme Economic Catastrophes; 3 Rare Events; 3.1 Standard Decision Theory; 3.2 Infinitesimal Probability; 3.3 Rare Events and Infinitesimal Probabilities; 3.4 A Metric Completion; 3.5 Extended Probability Measures; 3.6 Extended Subjective Expected Utility; 3.7 Lexicographic Expected Utility; 4 Black Swans.
4.1 Background4.2 Black Swan Events; 4.3 An Initial Simple Tree; 4.4 Initial Evaluation; 4.5 Enriched Subtrees; 4.6 Retrospective Evaluation in the Enlivened Tree; 4.7 Cardinally Equivalent Evaluation Functions; 4.8 Uncertain Retrospective Evaluation; 4.9 State-Dependent Consequence Domains; 4.10 Subjective Expected Evaluation; 4.11 Hubris Versus Enlivenment; 4.12 Could There Be a Metamodel?; 4.13 Should We Look for a Meta Stochastic Process?; 5 Concluding Remarks; References; Preference Representations for Catastrophic Risk Analysis; 1 Introduction; 1.1 The Problem; 1.2 Some Modeling Issues.
1.3 What We Do2 Minimal Model of Catastrophic Risk; 2.1 Illustrative Examples; 3 Alternative Models; 3.1 `Behavioral Probabilities' and `Ambiguity'; 3.2 #x8D;Sensitivity to Rare Events: A Topology of Fear#x8E;; 3.3 Variational Preferences: An Umbrella Model?; 4 Lessons and Conclusions; 5 Appendix: Axiomatic Foundations of Representations; 5.1 Notation; 5.2 Axioms; References; Modeling Decisions Involving Ambiguous, Vague, or Rare Events; 1 Topological Event Spaces; 2 Boundaries of Topological Events; 3 Application to Judgments of Probability; 4 Rationality; 5 Connections; References.
Modeling Uncertainty, Context, and Information Fusion via Lattice-Based Probability1 Introduction; 1.1 Upper-Lower Probability Theory; 1.2 Non-Boolean Algebra with Pseudo-complementation; 1.3 Why Lattice?; 2 Mathematical Background; 2.1 An Introduction to Lattice Theory; 2.2 Distributive Lattice; 2.3 Probability and Belief Functions on Lattice; 3 Upper-Lower Probability Anchored on Topology; 3.1 Topologizing Dempster-Shafer Theory; 3.2 Lattice of Topologies; 3.3 A Hierarchical Scheme for Upper-Lower Probability; 4 Discussions; 4.1 Relation to Topological Characterization of ``Rare Events''
1.1 Countably Additive Subjective Probability1.2 Monotonicity; 1.3 Beyond Monotonicity; 1.4 Outline of Paper; 2 Catastrophic Risk; 2.1 Etymology; 2.2 Catastrophic Consequences; 2.3 Assumptions; 2.4 Money Metric Utility; 2.5 A Critical Probability Level: Catastrophic Risk; 2.6 Extreme Economic Catastrophes; 3 Rare Events; 3.1 Standard Decision Theory; 3.2 Infinitesimal Probability; 3.3 Rare Events and Infinitesimal Probabilities; 3.4 A Metric Completion; 3.5 Extended Probability Measures; 3.6 Extended Subjective Expected Utility; 3.7 Lexicographic Expected Utility; 4 Black Swans.
4.1 Background4.2 Black Swan Events; 4.3 An Initial Simple Tree; 4.4 Initial Evaluation; 4.5 Enriched Subtrees; 4.6 Retrospective Evaluation in the Enlivened Tree; 4.7 Cardinally Equivalent Evaluation Functions; 4.8 Uncertain Retrospective Evaluation; 4.9 State-Dependent Consequence Domains; 4.10 Subjective Expected Evaluation; 4.11 Hubris Versus Enlivenment; 4.12 Could There Be a Metamodel?; 4.13 Should We Look for a Meta Stochastic Process?; 5 Concluding Remarks; References; Preference Representations for Catastrophic Risk Analysis; 1 Introduction; 1.1 The Problem; 1.2 Some Modeling Issues.
1.3 What We Do2 Minimal Model of Catastrophic Risk; 2.1 Illustrative Examples; 3 Alternative Models; 3.1 `Behavioral Probabilities' and `Ambiguity'; 3.2 #x8D;Sensitivity to Rare Events: A Topology of Fear#x8E;; 3.3 Variational Preferences: An Umbrella Model?; 4 Lessons and Conclusions; 5 Appendix: Axiomatic Foundations of Representations; 5.1 Notation; 5.2 Axioms; References; Modeling Decisions Involving Ambiguous, Vague, or Rare Events; 1 Topological Event Spaces; 2 Boundaries of Topological Events; 3 Application to Judgments of Probability; 4 Rationality; 5 Connections; References.
Modeling Uncertainty, Context, and Information Fusion via Lattice-Based Probability1 Introduction; 1.1 Upper-Lower Probability Theory; 1.2 Non-Boolean Algebra with Pseudo-complementation; 1.3 Why Lattice?; 2 Mathematical Background; 2.1 An Introduction to Lattice Theory; 2.2 Distributive Lattice; 2.3 Probability and Belief Functions on Lattice; 3 Upper-Lower Probability Anchored on Topology; 3.1 Topologizing Dempster-Shafer Theory; 3.2 Lattice of Topologies; 3.3 A Hierarchical Scheme for Upper-Lower Probability; 4 Discussions; 4.1 Relation to Topological Characterization of ``Rare Events''