Form Of Utility Function Research Articles

Utility-implied term structures of equity risk premia

The fundamental asset pricing problem is extended to the frequency domain for commonly used utility functional forms. For each class of utility functions, closed-form solutions are presented for the term structure of the equity risk premium. The term structure is flat for time separable one-period utility and uncorrelated external habit formation utility, downward sloping for internal habit formation utility, upward sloping for time preference (recursive) utility, and can be upward sloping, downward sloping, or flat for production-based utility. These results suggest how observed risk premium term structures can be mapped to linear time series models consistent with utility preference classes.

Policy Formulation for an Optimal Level of Savings in a Dynamic Setting

Objective: Previous literature on optimal savings relies on specific utility and production technology functional forms which might not be able to produce robust results as different utility / production functions may lead to dramatically different or opposing results. This paper derives an optimal savings policy based on parameters (such as slopes of demand and supply curves) which can be empirically estimated and provides a unique and robust result irrespective of shape and form of individual utilities / production functions. Furthermore, existing literature does not consider welfare loss when savings market is adjusting to final equilibrium after a shock while deriving an optimal savings policy. In addition to that, number of savers (all public and private saving entities, including households, firms, etc.) and saving rate are vital parameters for savings in an economy, and while deriving an optimal savings policy, it is necessary to take into consideration these parameters to ensure that quantum of savings due to interest rate movement gets adjusted in target time duration, without which there may be additional efficiency loss than that envisioned while deriving an optimal savings policy for an economy. Methods: This research project designs a dynamical model for savings market and extends that to a three-dimensional savings system in an economy by taking into consideration number of savers, saving rate, and interest rate; and based on that derives an optimal comprehensive savings policy while accounting for efficiency losses when savings market, saving rate, and number of savers are adjusting to final equilibrium, in addition to the welfare loss on account of equilibrium shift. Results: Without consideration of welfare loss / gain while savings market is adjusting after implementation of a savings policy, welfare picture remains incomplete, and the optimal savings policy based on partial welfare cannot be considered as optimal in true sense. Traditionally, welfare of only producer and consumer is taken into consideration without accounting for welfare of production factors. An expression of efficiency loss / gain as a result of savings policy based on welfare including those of production factors has been presented and optimal savings policies have been derived by minimizing efficiency losses and presented as a final result in the form of mathematical expressions. This paper demonstrates that both supply and demand shocks operate through a common channel, i.e., inventory of funds in savings market as both kinds of shock affect inventory of funds and hence can be categorized just as an inventory shock. Conclusion: For optimal welfare gains, practitioners / policy makers must estimate theoretically derived optimal savings policies based on the dynamic model developed in this paper and presented in the form of mathematical expressions from real world relevant data for implementation.

On Correlation Aversion and Insurance Demand

This is a study of decision problems under two-dimensional risk. We use an existing index of absolute correlation aversion to conveniently classify bivariate preferences, with respect to attitudes toward this risk. This classification seems to be more important than whether decision makers are correlation-averse or correlation-seeking for the study of insurance demand when a loss has a multidimensional impact. On this note, we also re-examine Mossin’s theorem under bivariate preferences, where full insurance is preferred with a fair premium, while less than full coverage is preferred with a proportional premium loading. Furthermore, based on the comparative statics of this two-dimensional insurance model for changes in correlation aversion, we derive testable implications about the classification of bivariate utility functions. For the particular case when the two-dimensional risk can be interpreted as risk on income and health, we identify the form of separable utility functions depending on health status and income that is consistent with household disability insurance decisions.

Development of Multiple Discrete-Continuous Extreme Value Model with Non-Monotonic Utilities: Formulation and Application to Outdoor Non-Mandatory Time-Use Decisions

This paper further explores multiple discrete-continuous extreme value (MDCEV) models. MDCEV models are widely used for time-use analysis because they can accommodate the diminishing marginal utility with respect to time consumption and benefit from simple closed-form likelihood expressions for estimation, while considering the overall constraints of time resource. However, all of the existing models adopt a monotonically increasing form of utility function, which does not accommodate possible non-monotonic utilities with respect to time-use. This paper further develops the MDCEV model by firstly introducing utility functions with a form of parabola to capture non-monotonic preferences in time allocation behaviors. A corresponding simple and computationally efficient forecasting algorithm to predict the time-use of individuals is also developed. The proposed MDCEV model with parabolic utilities is applied to analyze time-use decisions among a variety of outdoor non-mandatory activities on weekends using data from the 2019 American Time Use Survey. The proposed model is compared with traditional MDCEV models to show its ability to describe non-monotonic preferences in time-use in association with various explanatory variables. This paper makes an initial attempt to specify non-monotonic utilities for time-use analysis, but further studies are required to develop more sophisticated non-monotonic utility formulation to improve the goodness-of-fit of the model.

Optimal Growths from Two Perspectives, with Conditional Macro- and Micro-consistency: Dynamic Summation of Economic Variables Under Differential Regional Representative Production Functions

AbstractAlthough the representative theory of consumer/firm is widely used in particular forms of utility and production functions, is the optimal growth model adequately supported by a multi-regional microeconomic base in a “general form of utility and production functions”? Is the “optimization of macro-aggregate functions” consistent with the “summation of micro-optimal outcomes”? Economists have explored the problem of summation of macro-variables in a special form of production and utility function setting to find some theoretical foundations of macroeconomics in the case of heterogeneous representative consumers. However, heterogeneous representative producers have not been studied enough, and the conclusions are too dependent on the functional form. This study searches for the conditions for macroeconomics to reach micro-foundations in the framework of heterogeneous producers and general functions. Linking the entire macroeconomy through inter-regional capital flows, we distinguish between using and equity capital, construct a multi-regional dynamic optimal growth model in a homogeneous representative consumer and heterogeneous representative manufacturers, compare the summation of the regional dynamics with the aggregate macro-dynamics, and find that (A) the regional and macro-perspectives are generally inconsistent in their optimization results; (B) if the population growth rate is the same across regions, the macro-steady state is a weighted summation of the steady states; and (C) if the inverse of the absolute risk aversion is linearly additive to consumption, the model is reliable. In particular, CARA and CRRA-type utility functions are eligible. The eligible utility function can only be an exponential utility function or a power function utility function (the logarithmic utility function can be considered a degenerate power function utility).

Random “Decision and Experienced Utility”, Adaptive “Consumer Memory and Choice”: The Impact of Mind Fluctuations and Cognitive Biases on Consumption and Classification

In the study of consumer behavior, we believe that a distinction should be made between the subjective mental activity of consumption and the objective process of consumption experience, and that the deviation and fluctuation of “decision utility” and the randomness of “experience utility” have essential effects on consumer behavior. For one thing, purchase often precedes experience, and consumers cannot precisely predict utility and its distribution but can only make decisions based on adaptive expectations. Secondly, there is often uncertainty in the experience of goods, making predictions more difficult. Thirdly, the revision of consumer decision utility is carried out through memory in an adaptive process. We introduce two stochastic forms of decision and experience utility functions and build a two-period model. In the model, consumers make decisions based on a pre-determined decision utility function in the first period and a randomly realized experience utility function in the second period. The analysis shows that the volatility of “decision utility” and “experience utility” affects consumers in opposite directions; the former may trigger expansionary consumption, while the latter makes consumers more cautious. Finally, the consumption behaviors in the model can be divided into 24 categories based on the dimensions of chance, systematicity, luck, and deviance, corresponding to various scenarios. The total number of consumer behavior categories is a full ranking of the size relationship of the four factors mentioned above, thus 24 categories. For example, when good luck is accompanied by chance underestimation versus systematic underestimation, it leads to a better process experience for the consumer.

Space Invaders: Pedestrian Proxemic Utility Functions and Trust Zones for Autonomous Vehicle Interactions

Understanding pedestrian proxemic utility and trust will help autonomous vehicles to plan and control interactions with pedestrians more safely and efficiently. When pedestrians cross the road in front of human-driven vehicles, the two agents use knowledge of each other’s preferences to negotiate and to determine who will yield to the other. Autonomous vehicles will require similar understandings, but previous work has shown a need for them to be provided in the form of continuous proxemic utility functions, which are not available from previous proxemics studies based on Hall’s discrete zones. To fill this gap, a new Bayesian method to infer continuous pedestrian proxemic utility functions is proposed, and related to a new definition of ‘physical trust requirement’ (PTR) for road-crossing scenarios. The method is validated on simulation data then its parameters are inferred empirically from two public datasets. Results show that pedestrian proxemic utility is best described by a hyperbolic function, and that trust by the pedestrian is required in a discrete ‘trust zone’ which emerges naturally from simple physics. The PTR concept is then shown to be capable of generating and explaining the empirically observed zone sizes of Hall’s discrete theory of proxemics.

Pairwise stable networks in homogeneous societies with weak link externalities

We study general properties of pairwise stable and pairwise Nash stable networks when players are ex-ante homogeneous. Rather than assuming a particular functional form of utility, we impose general link externality conditions on utility such as ordinal convexity and ordinal strategic complements. Depending on these rather weak notions of link externalities, we show that pairwise Nash stable networks of various structure exist. For stronger versions of the convexity and strategic complements conditions, we are even able to characterize all pairwise stable networks: they are nested split graphs. We illustrate these results with many examples from the literature, including utility functions that arise from games with strategic complements played on the network and utility functions that depend on centrality measures such as Bonacich centrality.

Gain/loss asymmetric stochastic differential utility

This study examines a gain/loss asymmetric utility in continuous time in which the investor discounts their utility gain by more than the utility loss. By employing the theory of stochastic differential utility, the model allows an endogenously time-varying subjective discount rate. In addition, the model can express various forms of utility functions including a version of the Epstein–Zin utility. Under the model, even if the state variables do not have any jump in their paths, the optimal consumption/wealth ratio and portfolio weight can change non-smoothly.

Multi-period mean-variance portfolio selection with practical constraints using heuristic genetic algorithms

Since Markowitz proposed the mean-variance (MV) formulation in 1952, it has been used to configure various portfolio selection problems. However Markowitz's solution is only for a single period. Multi-period portfolio selection problems have been studied for a long time but most solutions depend on various forms of utility function, which are unfamiliar to general investors. Some works have formulated the problems as MV models and solved them analytically in closed form subject to certain assumptions. Unlike analytical solutions, genetic algorithms (GA) are more flexible because they can solve problems without restrictive assumptions. The purpose of this paper is to formulate multi-period portfolio selection problems as MV models and solve them by GA. To illustrate the generality of our algorithm, we implement a program by Microsoft Visual Studio to solve a multi-period portfolio selection problem for which there exists no general analytical solution.

Multi-period mean-variance portfolio selection with practical constraints using heuristic genetic algorithms

Since Markowitz proposed the mean-variance (MV) formulation in 1952, it has been used to configure various portfolio selection problems. However Markowitz's solution is only for a single period. Multi-period portfolio selection problems have been studied for a long time but most solutions depend on various forms of utility function, which are unfamiliar to general investors. Some works have formulated the problems as MV models and solved them analytically in closed form subject to certain assumptions. Unlike analytical solutions, genetic algorithms (GA) are more flexible because they can solve problems without restrictive assumptions. The purpose of this paper is to formulate multi-period portfolio selection problems as MV models and solve them by GA. To illustrate the generality of our algorithm, we implement a program by Microsoft Visual Studio to solve a multi-period portfolio selection problem for which there exists no general analytical solution.

An extended form of quasilinear utility functions

We show an extended form of quasilinear utility functions, which is characterized by the Gorman polar form and the property that a consumer surplus, a compensating variation, and an equivalent variation coincide for the changes of prices and income under a certain condition.

Cache Me if You Can: Capacitated Selfish Replication Games in Networks

In Peer-to-Peer (P2P) network systems, content (object) delivery between nodes is often required. One way to study such a distributed system is by defining games, which involve selfish nodes that make strategic choices on replicating content in their local limited memory (cache) or accessing content from other nodes for a cost. These Selfish Replication games have been introduced in Chun et al. (2004) for nodes that do not have any capacity limits, leaving the capacitated problem, i.e. Capacitated Selfish Replication (CSR) games, open. In this work, we first form the model of the CSR games, for which we perform a Nash equilibria analysis. In particular, we focus on hierarchical networks, given their extensive use to model communication costs of content delivery in P2P systems. We present an exact polynomial-time algorithm for any hierarchical network, under two constraints on the utility functions: 1) “Nearer is better”, i.e. the closest the content is to the node the less its access cost is, and 2) “Independence of irrelevant alternatives”, i.e. aggregation of individual node preferences. This generalization represents a vast class of utilities and more interestingly allows each of the nodes to have simultaneously completely different functional forms of utility functions. In this general framework, we present CSR games results on arbitrary networks and outline the boundary between intractability and effective computability in terms of the network structure, object preferences, and the total number of objects. Moreover, we prove that the problem of equilibria existence becomes NP-hard for general CSR games. By adding some constraints in the number of objects and their preferences, we show that the equilibrium can be found in polynomial time. Finally, we introduce the fractional version of CSR games (F-CSR) to represent content distribution. We prove that equilibrium exists for every F-CSR game, but it is PPAD-complete.

A game theoretic approach to optimize multi-stakeholder utilities for land acquisition negotiations with informality

To combat the critical stresses of rising urbanization, the government acquires land from private owners using the power of eminent domain. This land assembly causes negative externalities such as increasing social tension and injustice that may impose a long-term threat to stability and sustainable development. Therefore, there is a need to make the land acquisition process more transparent and just. Considering the unique Indian context where informality has a strong presence, we propose an approach based on game theory that models the bargain through a three-stage Nash equilibrium game. Four agents – the government, the private developer, the landowner, and the free rider – are considered. We provide conditional solutions for the generalizable Case and proceed to model different stakeholder behavior patterns through two utility functional forms – linear and exponential. In the linear case, we find that the free rider obtains half of the revenue of the project, whereas the landowner gains between one-fourth and one-half of the revenue. Thus, we highlight the undeniably crucial role free riders play in land acquisition negotiations. However, closed form solutions cannot be obtained for the exponential form, due to which we use simulations to demonstrate a solution procedure. We conclude by stating that the proposed model can be useful in formulating future land policies in a sustainable and inclusive manner, with optimal utility derivations for all concerned stakeholders. Our model can also be extended to other spatial contexts where informality features heavily in the land market, especially in the Global South.

Higher-order Omega: A performance index with a decision-theoretic foundation

Abstract This paper proposes a new performance index referred to as the Nth-order Omega that includes the well-known Omega as a special case. The index is established by adopting an approach that is free of a utility functional form or/and distributional assumptions. A decision-theoretic foundation for our index is further established through introducing a new distribution ranking criterion. The index is monotonic with respect to Nth-degree stochastic dominance and offers a complete ordering on gambles. An empirical example of deriving the optimal hedge ratio is demonstrated to show the applicability of the index.

Zero-rating Internet platforms formation: a game theoretic analysis

Zero-rating Internet is a term that is used for not counting data usage of end-users for accessing basic capabilities of some websites via mobile network operators. Recently, an open zero-rating platform called Free Basics is offered by Facebook which in addition to providing free basic services of Facebook to the end-users, it allows other websites to provide their contents as zero-rated through the platform for free. In this paper, we provide a game theoretic analysis to investigate the reasons behind the formation of fully or partially open zero-rating platforms such as Free Basics. For this purpose, a variant of a specific dynamic game called asymmetric volunteer’s timing dilemma is used to model zero-rating platforms formation with content providers as the players. The general solution of the game is determined as a form of sub-game perfect Nash equilibrium (SPNE). Moreover, specific forms of utility functions for content providers are introduced with consideration of network effects to draw SPNE of the game and demonstrate the behaviors of the involved parameters in the game results. The modeling and its solution helps us to explain current state of the zero-rating platforms and its stability. In particular, our result is in accord with the formation of Free Basics platform by Facebook.

Модель реального сектора российской экономики с несколькими продуктами и агентами-торговцами

In this paper a real sector model of Russian economy is presented based on multiproduct decomposition of macroeconomic statistic. Model allows to reproduce statistic accurately in constant and current prices which is not possible in many other macroeconomic models.Model economy consists of agent-traders with the help of which GDP and its components are decomposed into unobservable products, agent-producer and agent-consumer. Traders are described by CES-functions. Analytical solution of trader problem gives ratios that are used for GDP decomposition.Producer has specific production function in which are considered two types of investments - investments that support fixed assets and investments that help to build up fixed assets. In addition, labor demand is described using an original scheme. Moreover, stock formation is described in producer model which is usually omitted in standard macroeconomic models.Aggregate consumer model reproduces optimal trajectories for consumption, labor and consumer deposits. Specific form of utility function gives opportunity to include labor as endogenous variable in the model which is not usually made in standard macroeconomic models. Considering economically active population and modifying calibration function it is possible to receive high accuracy in reproducing consumption, labor and deposits trajectories even in crisis periods.In this paper models are analytically solved and calibrated on real data without linearization procedure.

A generalized game theoretic framework for mining communities in complex networks

Since the community structure is able to reveal the potential law behind complex networks, mining hiding communities has gained particular attention from various applications. A variety of objective functions, such as Modularity, weighted clustering coefficient (WCC), etc., have been developed to characterize the cohesiveness of a community, and thus many community detection approaches are proposed by optimizing a predefined objective function. This paper offers a urgent study on how to integrate different objective functions into a generic framework, which aims to enhance the flexibility of expert systems that are designed to identify communities from complex networks. Specifically, we formulate the process of community detection as a strategic game and give a general form of utility function for each agent from the perspective of game theory. Furthermore, we prove that if the parameters in the generalized utility function can be specified carefully, the strategic game could well match a potential game and be able to converge to a pure Nash equilibrium. In addition, we choose some commonly used objective functions to match the generalized utility function and design a synchronous learning model to test the performance of different global models. Compared with existing approaches, experimental results on synthetic and real-world data sets demonstrate that the proposed model achieve higher accuracy and efficiency.

Clear Preferences Under Partial Distribution Information

Stochastic dominance is often used to study preference between different distributions of outcomes. In the stochastic dominance literature, distributions of outcomes are often assumed to be known. However, complete distribution information is rarely available in practice. In this paper, we study weighted almost first-degree stochastic dominance (WAFSD) under limited distribution information. In particular, we show that it is possible to determine WAFSD with linear canonical utility based on expected rewards when outcomes are bounded from below. Furthermore, we illustrate how WAFSD based on more general forms of canonical utility functions can be ensured when additional moment information is available. The key insight is that finite distribution moments can be sufficient for revealing clear preferences in practice, despite the fact that finite distribution moments are generally insufficient for ensuring preferences across all utility functions.

PUSH, PULL, AND POPULATION SIZE EFFECTS IN STRUCTURAL DEVELOPMENT: LONG-RUN TRADE-OFFS

Abstract:The process of structural transformation from the farm to a nonfarm sector is accompanied by technological change in both sectors and massive population growth. We investigate the effects of increasing population size (the population effect) and sector-specific productivity (the push and pull effects), both factor-neutral and factor-biased, in a parsimonious general equilibrium model under general forms of utility and production functions. All three effects may co-exist and interact in important ways. Generalizing the agricultural sector production function to CES is crucial for the population growth effect. Our analysis highlights how the relative importance of the three effects changes as the country develops and production and consumption conditions become more flexible.