Discounting models for outcomes over continuous time

Events that occur over a period of time can be described either as sequences of outcomes at discrete times or as functions of outcomes in an interval of time. This paper presents discounting models for events of the latter type. Conditions on preferences are shown to be satisfied if and only if the preferences are represented by a function that is an integral of a discounting function times a scale defined on outcomes at instants of time.     

Repeated games in continuous time as extensive form games

Extensive form games modeling continuous-time decisions are plagued with problems of nonexistence and nonuniqueness of outcomes. As a “second-best”, the literature has imposed extraneous restrictions on the strategy sets, raising questions on the nature and interpretation of the resulting formal object, and on which restrictions are appropriate. We provide a “first-best” framework, formalizing continuous-time repeated games as extensive form games incorporating natural conditions from the onset. Every strategy profile induces a unique outcome, without any restrictions on the strategy sets. Further, the unrestricted strategy sets are equivalent to a specific class of strategies in a more naïvely specified continuous-time game.     

Production technologies in stochastic continuous time models

Properties of dynamic stochastic general equilibrium models can be revealed by either using numerical solutions or qualitative analysis. Very precise and intuition-building results are obtained by working with models which provide closed-form solutions. Closed-form solutions are known for a large class of models some of which, however, have some undesirable features such as potentially negative output. This paper offers closed-form solutions for models which are just as tractable but do not suffer from these shortcomings.     

Continuous time vs. backward induction a new approach to modelling reputation in the finite time horizon context

This paper suggests a new approach to modeling credible reputation in the finite time horizon context, using continuous time and interactions which arrive via a Poisson process. Behavior in the present model does not depend on small ad hoc irrationalities as the end of the horizon nears, and the model preserves the intuitive result that as the end of the horizon nears, the level of reputation declines towards zero. While the current paper considers the predatory pricing case, the approach should also apply whenever reputation and/or cooperation are important.     

Time-inconsistent preferences and social security: Revisited in continuous time

?mrohoro?lu et al. (2003) prove that it is impossible in a three period partial equilibrium model for social security to improve the welfare of a naive quasi-hyperbolic agent if the program has a negative net present value. This paper first generalizes their impossibility theorem to a continuous time setting and then proves analytically that no discount function exists that can rationalize a social security program with a negative net present value.     

Management of a capital stock by Strotz's naive planner

The capital management problem posed by R.H. Strotz is analyzed for the case of the ‘naive’ planner who fails to anticipate changes in his own preferences. By imposing progressively stronger restrictions on the primitives of the problem – namely, the discounting function, the utility index function, and the investment technology – the planner's behavior is characterized first as the solution to an ordinary differential equation and then via explicit formulae. Inasmuch as these characterizations leave the discounting function essentially unrestricted, the theory can accommodate, in particular, decision makers who discount time according to the hyperbolic and ‘quasi-hyperbolic’ curves used in applied work and said to be supported by psychological studies. Comparative statics of the model are discussed, as are extensions of the analysis to allow for credit constraints, limited foresight, and partial commitment.     

Monitoring the cross-covariances of a multivariate time series

In this paper sequential procedures are proposed for jointly monitoring all elements of the covariance matrix at lag 0 of a multivariate time series. All control charts are based on exponential smoothing. As a measure of the distance between the target values and the actual values the Mahalanobis distance is used. It is distinguished between residual control schemes and modified control schemes. Several properties of these charts are proved assuming the target process to be a stationary Gaussian process. Within an extensive Monte Carlo study all procedures are compared with each other. As a measure of the performance of a control chart the average run length is used. An empirical example about Eastern European stock markets illustrates how the autocovariance and the cross-covariance structure of financial assets can be monitored by these methods.     

Revealed preferences of individual players in sequential games

This paper studies rational choice behavior of a player in sequential games of perfect and complete information without an assumption that the other players who join the same games are rational. The model of individually rational choice is defined through a decomposition of the behavioral norm assumed in the subgame perfect equilibria, and we propose a set of axioms on collective choice behavior that characterize the individual rationality obtained as such. As the choice of subgame perfect equilibrium paths is a special case where all players involved in the choice environment are each individually rational, the paper offers testable characterizations of both individual rationality and collective rationality in sequential games.     

Monitoring the mean and the variance of a stationary process

We deal with the problem of how deviations in the mean or the variance of a time series can be detected. Several simultaneous control charts are introduced which are based on EWMA (exponentially weighted moving average) statistics for the mean and the empirical variance. The combined X − S² EWMA chart is extended to time series. Further simultaneous charts are considered. The comparision of these schemes shows that the residual attempt must be favored if a variance change is present.     

Diversity of preferences in an unpredictable environment

The origin of preferences was viewed as related to the dominant eigenvalue of a Leslie matrix modelling reproductive strategies. In a variable environment, however, the coexistence of varying preferences no longer requires optimality, but is identified with the mathematical property of viability: a state of the population is viable if there exists at least one solution starting from it and remaining in the set of constraints until a given time horizon (or forever).The coexistence kernel of two competitors with varying preferences is computed for the case of scalar and 2 × 2 Leslie matrices, with either measurable or differentiable preferences. The homologue of indifference curves is the regulation map, the correspondence associating the set of viable preferences to a given state of the population.Among these viable trajectories, some are also optimal in the sense of dominance discounted in time. These viable optimal solutions are obtained as specific trajectories in an auxiliary dynamic system, and the associated maximal values constitute one boundary of the viability kernel of this auxiliary system (theorem). Hence, the perpetuation of varying preferences allows the diversity of economic preferences, as shown here using the example of the comparative history of fertility from mid-nineteenth century to nowadays in France and England.     

Evolution of preferences and cross-country differences in time devoted to market work

I model the hypothesis that preferences evolve and permanent differences in individual attitudes towards work emerge between two countries characterized initially by identical preferences as a result of a period in which only one of the two countries is subject to regulations constraining labor supply, or as a by-product of different tax rates on labor income. Hence, the elimination of these regulations may not allow the economy thus deregulated to converge to the same hours of market work per person of the other economy, and the long-run differential in market work between economies subject to different tax rates is amplified.     

Management turnover expectations: a variable to explain company readiness to engage in continuous management training

What makes companies give their support to Continuous Management Training (CMT) and why, on occasion, do they block its progress? If a company thinks its managers might leave in the near future, would there be reasons for it to provide continuous training of these professionals? Do companies interpret all likely resignations in the same way? We attempt to provide an answer to these questions, by analysing the behaviour of companies' vis-à-vis continuous management training in terms of their expectations of the appropriability of the benefits that stem from such training. Appropriability is in turn assessed with regard to firms' expectations that their managers will leave their organisation without it having had the chance to recover the outlay invested in training. The analysis of business behaviour also demands an understanding of how these turnover expectations are produced and, more specifically, of the variables on which turnover expectations depend or might depend. The empirical study we carried out with over 300 Spanish companies revealed that company projections for voluntary turnover of management employees are positively connected with earlier experiences of turnover, with markets prone to change, and with business risk situations, and negatively associated with developed social management networks, satisfied managers and their degree of specificity in relation to the company. Nevertheless, no significant relationship was observed between expected turnover and the intensity of continuous management training. In general, companies make their management training investment decisions independently of the overall turnover expectations they might have. Different causes might exist for this absence of a relationship, centred in particular on the need for management training and an associated sense of urgency, which takes precedence over the risk of not recovering the investment when the business decision is taken, and on the nature of the management turnover perceived by the company, which is more complex than a strictly economic one.     

Ambulance response time in a Brazilian emergency medical service

Research efforts on ambulance response times for Emergency Medical Services (EMS) calls have been made for decades, especially in developed countries, using different techniques and with varying objectives. In Brazil, a developing country, the scarce scientific production on this vital indicator prioritizes scenarios for EMS in cities with more than one million inhabitants. This shows the importance of extending research to the reality of small and medium-sized cities. This paper presents SAMU, the Brazilian EMS that follows the Franco-German emergency medicine model, compiling numbers related to service at the national level. The use of quantile regression allows the identification of the RT for the EMS and helps to explain the effects of factors at the system level, at the patient level, and specific factors on response time intervals of Southwest Paraná SAMU. This specific EMS, characterized as an inter-municipal consortium of prehospital services, is responsible for prehospital emergency care for an approximate population of 635,000 inhabitants in 42 small towns in the State of Paraná in southern Brazil. From the analysis of the records of 12,050 ambulance dispatches, it was possible to identify the average ambulance response time of 14 min and 25 s. The regression model was able to explain the influence of the independent variables at the system level (presumed severity of the emergency, ambulance dispatch time, and ambulance travel time), at the patient level (age, gender, and characteristic of the emergency) and specific variables of the emergency (day of the week and time of day) on the dependent variable response time over the quantiles, showing that the dispatch time, travel time, time of day, service to male patients and critical cases influence the ambulance response time. This work contributes to deepening the understanding of the management of EMS operations in a developing country, allows the comparison of the RT identified in relation to other countries, and identifies factors that impact the RT for other actors directly or indirectly involved. The practical implications are also presented, as well as how the study impacts the decision-making and management process of the EMS in the short, medium and long term.     

Market selection of constant proportions investment strategies in continuous time

This paper studies the wealth dynamics of investors holding self-financing portfolios in a continuous-time model of a financial market. Asset prices are endogenously determined by market clearing. We derive results on the asymptotic dynamics of the wealth distribution and asset prices for constant proportions investment strategies. This study is the first step towards a theory of continuous-time asset pricing that combines concepts from mathematical finance and economics by drawing on evolutionary ideas.     

Parameter estimation for the drift of a time inhomogeneous jump diffusion process

This work deals with parameter estimation for the drift of jump diffusion processes which are driven by a Lévy process and whose drift term is linear in the parameter. In contrast to the commonly used maximum likelihood estimator, our proposed estimator has the practical advantage that its calculation does not require the evaluation of the continuous part of the sample path. In the important case of an Ornstein‐Uhlenbeck‐type jump diffusion, which is a widely used model, we prove consistency and asymptotic normality.     

The mean-variance investment problem in a constrained financial market

This paper extends the mean-variance analysis and the two-fund separation theorem to a market with some constraints, such as, the incompleteness, prohibition of short-selling, and partial information, with stochastic interest rate, and with stochastic volatility for risky assets. By maximizing a quadratic utility of terminal wealth, we show that the efficient frontier for the problem is a straight line in the mean-standard-deviation diagram. The quadratic utility function exhibits mean-variance efficiency. Our results apply to portfolios of claims in a single period, multiperiod, and continuous time.     

Existence of financial equilibria in continuous time with potentially complete markets

We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.     

Optimal harvesting of a spatial renewable resource

In this paper we investigate the optimal harvesting of a renewable natural resource. While in most standard approaches the resource is located at a single point, we allow the resource to be distributed spatially. Consequently, an agent who exploits the resource has to travel from one location to another. For a fixed planning horizon, we investigate the speed and the path of harvesting chosen by the agent. We show that the agent adjusts this speed so as to visit each location only once, even in the absence of travelling cost. Since the agent does not return to any location for a second harvest, it is optimal to fully deplete the resource upon arrival. A similar type of bang–bang solution results when we drop the assumption of a constant harvesting rate: allowing for a variable harvesting rate, the agent chooses to fully exploit the resource either in the last or in the first travelling period. A society interested in conserving some of the resource thus has to take measures to limit the exploitative behaviour of the agent.     

企业时间成本管理的制度分析

改革开放以来,我国企业的成本管理方法获得了长足的进步,但是对于时间成本管理,目前还处于研究的起步阶段。文章尝试从制度的角度出发分析时间成本问题的起因及其与企业效率、效益的作用机制,认为路径依赖和制度供给不足是时间成本问题产生和存在的主要原因,并从正式制度和非正式制度的角度给出了若干实施时间成本管理的制度创新途径。