General equilibrium

Unlike partial equilibrium analysis which study the equilibrium of a particular market under the clause "ceteris paribus" that revenues and prices on the other markets stay approximately unaffected, the ambition of a general equilibrium model is to analyze the simultaneous equilibrium in all markets of a competitive economy. Definition of the abstract model, some of its basic results and insights are presented. The important issues of uniqueness and local uniqueness of equilibrium are sketched ; they are the condition for a predictive power of the theory and its ability to allow for statics comparisons. Finally, we review the main extensions of the general equilibrium model. Besides the natural extensions to infinitely many commodities and to a continuum of agents, some examples show how economic theory can accommodate the main ideas in order to study some contexts which were not thought of by the initial model.Commodity space, price space, exchange economy, production economy, feasible allocations, equilibrium, quasi-equilibrium, Pareto optimum, core, edgeworth equilibrium allocutions, time and uncertainty, continuum economies, non-convexities, public goods, incomplete markets.

Insurance with multiple insurers: A game-theoretic approach

This paper studies the set of Pareto optimal insurance contracts and the core of an insurance game. Our setting allows multiple insurers with translation invariant preferences. We characterise the Pareto optimal contracts, which determines the shape of the indemnities. Closed-form and numerical solutions are found for various preferences that the insurance players might have. Determining associated premiums with any given optimal Pareto contract is another problem for which economic-based arguments are further discussed. We also explain how one may link the recent fast growing literature on risk-based optimality criteria to the Pareto optimality criterion and we show that the latter is much more general than the former one, which according to our knowledge, has not been pointed out by now. Further, we extend some of our results when model risk is included, i.e. there is some uncertainty with the risk model and/or the insurance players make decisions based on divergent beliefs about the underlying risk. These robust optimal contracts are investigated and we show how one may find robust and Pareto efficient contracts, which is a key decision-making problem under uncertainty

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences

The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as patience, socialization effects, and market volatility. The market is composed of multiple risky assets and multiple consumption goods, while in addition there are multiple fluctuating preference parameters with inexact values connected to imprecise tastes. Utility maximization is a multi-criteria problem with possibly function-valued criteria. To come up with a complete characterization of the solutions, first we motivate and introduce a set-valued stochastic process for the dynamics of multi-utility indices and formulate the optimization problem in a topological vector space. Then, we modify a classical scalarization method allowing for infiniteness and randomness in dimensions and prove results of equivalence to the original problem. Illustrative examples are given to demonstrate practical interests and method applicability progressively. The link between the original problem and a dual problem is also discussed, relatively briefly. Finally, using Malliavin calculus with stochastic geometry, we find optimal investment policies to be generally set-valued, each of whose selectors admits a four-way decomposition involving an additional indecisiveness risk-hedging portfolio. Our results touch on new directions for optimal consumption--investment choices in the presence of incomparability and time inconsistency, also signaling potentially testable assumptions on the variability of asset prices. Simulation techniques for set-valued processes are studied for how solved optimal policies can be computed in practice.Comment: 72 pages, 1 table, 13 figure

Quality Representation in Multiobjective Programming

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along the way, several interesting results about obtuse, simplicial cones are also proved. Both the BCS and CCS methods are tested and show promise on a variety of problems: linear, convex, nonconvex (CCS only), two-dimensional, and three-dimensional. Sample Matlab code for two of these examples can be found in the appendices as well as tables containing the generated solution points. The manuscript closes with conclusions and ideas for further research in this field

A Methodological Guide to Multiobjective Optimization

During the last few years, multiobjective optimization has received growing attention: the number of publications related to this subject between 1974 and 1979 exceeds 120. There are many approaches, techniques and tools related to multiobjective decision-making and optimization; however, not all approaches are equally developed, and the resulting tools are often applied because of certain traditions rather than their suitability for solving a given problem. Therefore, this paper is devoted to a comparative evaluation of various approaches and tools. This evaluation is based, however, first on a classification of problems of multiobjective decision making and optimization. Thereafter, the available approaches, methods, techniques and tools are shortly presented and evaluated in terms of suitability for various classes of problems. The final part of the paper presents a broader description of a relatively new approach based on reference objective levels, not fully developed yet but applicable in many classes of problems. A new notion of extended threshold utility functions, other basic theoretical results, applicational examples and directions of further research related to this approach are presented

General Equilibrium with Asymmetric Information: A Dual Approach

We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive trans- actions, the environment is described as a continuum economy with indivis- ible commodities. We characterize incentive constrained eÆcient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external e ects in these markets. Because under certain conditions such e ects may generate non-convexities, random- ization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external e ects may have critical implications for market eÆciency. With ad- verse selection, in fact, cross-subsidization across agents with di erent private information may be necessary for optimality, and so, the market need not even achieve an incentive constrained eÆcient allocation. In contrast, for the case of a single commodity, we nd that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external e ects are fully internalized at a market equilibrium