Ordering Pareto-Optima Through Majority Voting

A commodity is shared between some individuals; some selection procedure is used to choose allocations. In order to reflect that laws and rules rather than allocations are implemented and that they involve an element of randomness because of incomplete information, selection procedures are taken to be probability measures over the set of allocations. Illustrations and interpretations of the selection procedures are given.Pareto-optimal allocations; infra-majority voting

Asymptotic Existence of Proportionally Fair Allocations

Fair division has long been an important problem in the economics literature. In this note, we consider the existence of proportionally fair allocations of indivisible goods, i.e., allocations of indivisible goods in which every agent gets at least her proportionally fair share according to her own utility function. We show that when utilities are additive and utilities for individual goods are drawn independently at random from a distribution, proportionally fair allocations exist with high probability if the number of goods is a multiple of the number of agents or if the number of goods grows asymptotically faster than the number of agents

Load optimization in a planar network

We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and $n$ objects spatially uniformly distributed, each object being allocated to a bin at a cost depending on its position. Two allocations are considered: the allocation minimizing the bin loads and the allocation allocating each object to its less costly bin. We analyze the asymptotic properties of these allocations as the number of objects grows to infinity. Using the symmetries of the problem, we derive a law of large numbers, a central limit theorem and a large deviation principle for both loads with explicit expressions. In particular, we prove that the two allocations satisfy the same law of large numbers, but they do not have the same asymptotic fluctuations and rate functions.Comment: Annals of Applied Probability 2010, Vol. 20, No. 6, 2040-2085 Published in at http://dx.doi.org/10.1214/09-AAP676 the Annals of Applied Probability by the Institute of Mathematical Statistics (http://www.imstat.org) 10.1214/09-AAP67

The Evolution of Exchange

Stochastic stability is applied to the problem of exchange. We analyze the stochastic stability of two dynamic trading processes in a simple housing market. In both models traders meet in pairs at random and exchange their houses when trade is mutually beneficial, but occasionally they make mistakes. The models differ in the probability of mistakes. When all mistakes are equally likely, the set of stochastically stable allocations contains the set of efficient allocations. When more serious mistakes are less likely, the stochastically stable states are those allocations, always efficient, with the lowest envy-level.stochastic stability, exchange, housing problem, efficiency, envy.

Dynamic Recontracting processes with Multiple Indivisible Goods

We consider multiple-type housing markets. To capture the dynamic aspect of trade in such markets, we study a dynamic recontracting process similar to the one introduced by Serrano and Volij (2005). First, we analyze the set of recurrent classes of this process as a (non-empty) solution concept. We show that each core allocation always constitutes a singleton recurrent class and provide examples of non-singleton recurrent classes consisting of blocking-cycles of individually rational allocations. For multiple-type housing markets stochastic stability never serves as a selection device among recurrent classes. Next, we propose a method to compute the limit invariant distribution of the dynamic recontracting process. The limit invariant distribution exploits the interplay of coalitional stability and accessibility that determines a probability distribution over final allocations. We provide various examples to demonstrate how the limit invariant distribution discriminates among stochastically stable allocations: surprisingly, some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.microeconomics ;

The effects of systemic crises when investors can be crisis ignorant

Systemic crises can largely affect asset allocations due to the rapid deterioration of the risk-return trade-off. We investigate the effects of systemic crises, interpreted as global simultaneous shocks to financial markets, by introducing an investor adopting a crisis ignorant or crisis conscious strategy. Including the possibility of a systemic crisis is a substantial improvement. Investments in risky assets fall, while allocations to countries less sensitive to a crisis grow relatively. An increasing probability of a crisis exacerbates these effects. The certainty equivalent costs of ignoring systemic crises are large, ranging from 0.65% per year unconditionally, to over 5% per month conditionally on a high probability for the occurrence of a crisis.international finance;asset allocation;systemic risk;regime switching

Mistakes in cooperation: the stochastic stability of edgeworth's recontracting

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes -do not improve- in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochastically stable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process

Dynamic recontracting processes with multiple indivisible goods

We consider multiple-type housing markets. To capture the dynamic aspect of trade in such markets, we study a dynamic recontracting process similar to the one introduced by Serrano and Volij (2005). First, we analyze the set of recurrent classes of this process as a (non-empty) solution concept. We show that each core allocation always constitutes a singleton recurrent class and provide examples of non-singleton recurrent classes consisting of blocking-cycles of individually rational allocations. For multiple-type housing markets stochastic stability never serves as a selection device among recurrent classes.Next, we propose a method to compute the limit invariant distribution of the dynamic recontracting process. The limit invariant distribution exploits the interplay of coalitional stability and accessibility that determines a probability distribution over final allocations. We provide various examples to demonstrate how the limit invariant distribution discriminates among stochastically stable allocations: surprisingly, some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.core, indivisible goods, limit invariant distribution, stochastic stability

Capital market expectations, asset allocation, and safe withdrawal rates

Most retirement withdrawal rate studies are either based on historical data or use a particular assumption about portfolio returns unique to the study in question. But planners may have their own capital market expectations for future returns from stocks, bonds, and other assets they deem suitable for their clients’ portfolios. These uniquely personal expectations may or may not bear resemblance to those used for making retirement withdrawal rate guidelines. The objective here is to provide a general framework for thinking about how to estimate sustainable withdrawal rates and appropriate asset allocations for clients based on one’s capital market expectations, as well as other inputs about the client including the planning horizon, tolerance for exhausting wealth, and personal concerns about holding riskier assets. The study also tests the sensitivity of various assumptions for the recommended withdrawal rates and asset allocations, and finds that these assumptions are very important. Another common feature of existing studies is to focus on an optimal asset allocation, which is expected either to minimize the probability of failure for a given withdrawal rate, or to maximize the withdrawal rate for a given probability of failure. Retirement withdrawal rate studies are known in this regard for lending support to stock allocations in excess of 50 percent. This study shows that usually there are a wide range of asset allocations which can be expected to perform nearly as well as the optimal allocation, and that lower stock allocations are indeed justifiable in many cases.retirement planning; safe withdrawal rates; asset allocation; capital market expectations