A Universal Formula for Continuous Utility

A single formula assigns a continuous utility function to every representable preference relation.

Local Utility Functions and Local Probability Transformations

This note shows that, under appropriate conditions, preferences may be locally approximated by the linear utility or risk-neutral preference functional associated with a local probability transformation.

Decision theory applied to image quality control in radiology

Background: The present work aims at the application of the decision theory to radiological image quality control ( QC) in diagnostic routine. The main problem addressed in the framework of decision theory is to accept or reject a film lot of a radiology service. The probability of each decision of a determined set of variables was obtained from the selected films. Methods: Based on a radiology service routine a decision probability function was determined for each considered group of combination characteristics. These characteristics were related to the film quality control. These parameters were also framed in a set of 8 possibilities, resulting in 256 possible decision rules. In order to determine a general utility application function to access the decision risk, we have used a simple unique parameter called r. The payoffs chosen were: diagnostic's result (correct/incorrect), cost (high/low), and patient satisfaction (yes/no) resulting in eight possible combinations. Results: Depending on the value of r, more or less risk will occur related to the decision-making. The utility function was evaluated in order to determine the probability of a decision. The decision was made with patients or administrators' opinions from a radiology service center. Conclusion: The model is a formal quantitative approach to make a decision related to the medical imaging quality, providing an instrument to discriminate what is really necessary to accept or reject a film or a film lot. The method presented herein can help to access the risk level of an incorrect radiological diagnosis decision.

Life-cycle preferences over consumption and health: when is cost-effectiveness analysis equivalent to cost-benefit analysis?

This paper studies life-cycle preferences over consumption and health status. We show that cost-effectiveness analysis is consistent with cost-benefit analysis if the Lifetime utility function is additive over time, multiplicative in the utility of consumption and the utility of health status, and if the utility of consumption is constant over time. We derive the conditions under which the lifetime utility function takes this form, both under expected utility theory and under rank-dependent utility theory, which is currently the most important nonexpected utility theory. If cost-effectiveness analysis is consistent with cost-benefit analysis, it is possible to derive tractable expressions for the willingness to pay for quality-adjusted life-years (QALYs). The willingness to pay for QALYs depends on wealth, remaining life expectancy, health status, and the possibilities for intertemporal substitution of consumption. (C) 1999 Elsevier Science B.V. All rights reserved.

On a theorem of Cooper

In this paper we study some purely mathematical considerations that arise in a paper of Cooper on the foundations of thermodynamics that was published in this journal. Connections with mathematical utility theory are studied and some errors in Cooper's paper are rectified. (C) 2001 Academic Press.

A decision-support system based on particle swarm optimization for multiperiod hedging in electricity markets

This paper proposes a particle swarm optimization (PSO) approach to support electricity producers for multiperiod optimal contract allocation. The producer risk preference is stated by a utility function (U) expressing the tradeoff between the expectation and variance of the return. Variance estimation and expected return are based on a forecasted scenario interval determined by a price range forecasting model developed by the authors. A certain confidence level is associated to each forecasted scenario interval. The proposed model makes use of contracts with physical (spot and forward) and financial (options) settlement. PSO performance was evaluated by comparing it with a genetic algorithm-based approach. This model can be used by producers in deregulated electricity markets but can easily be adapted to load serving entities and retailers. Moreover, it can easily be adapted to the use of other type of contracts.

A long-term swarm intelligence hedging tool applied to electricity markets

This paper proposes a swarm intelligence long-term hedging tool to support electricity producers in competitive electricity markets. This tool investigates the long-term hedging opportunities available to electric power producers through the use of contracts with physical (spot and forward) and financial (options) settlement. To find the optimal portfolio the producer risk preference is stated by a utility function (U) expressing the trade-off between the expectation and the variance of the return. Variance estimation and the expected return are based on a forecasted scenario interval determined by a long-term price range forecast model, developed by the authors, whose explanation is outside the scope of this paper. The proposed tool makes use of Particle Swarm Optimization (PSO) and its performance has been evaluated by comparing it with a Genetic Algorithm (GA) based approach. To validate the risk management tool a case study, using real price historical data for mainland Spanish market, is presented to demonstrate the effectiveness of the proposed methodology.

A long-term risk management tool for electricity markets using swarm intelligence

This paper addresses the optimal involvement in derivatives electricity markets of a power producer to hedge against the pool price volatility. To achieve this aim, a swarm intelligence meta-heuristic optimization technique for long-term risk management tool is proposed. This tool investigates the long-term opportunities for risk hedging available for electric power producers through the use of contracts with physical (spot and forward contracts) and financial (options contracts) settlement. The producer risk preference is formulated as a utility function (U) expressing the trade-off between the expectation and the variance of the return. Variance of return and the expectation are based on a forecasted scenario interval determined by a long-term price range forecasting model. This model also makes use of particle swarm optimization (PSO) to find the best parameters allow to achieve better forecasting results. On the other hand, the price estimation depends on load forecasting. This work also presents a regressive long-term load forecast model that make use of PSO to find the best parameters as well as in price estimation. The PSO technique performance has been evaluated by comparison with a Genetic Algorithm (GA) based approach. A case study is presented and the results are discussed taking into account the real price and load historical data from mainland Spanish electricity market demonstrating the effectiveness of the methodology handling this type of problems. Finally, conclusions are dully drawn.

A comprehensive simulation study of slotted CSMA/CA for IEEE 802.15.4 wireless sensor networks

In this paper, we analyze the performance limits of the slotted CSMA/CA mechanism of IEEE 802.15.4 in the beacon-enabled mode for broadcast transmissions in WSNs. The motivation for evaluating the beacon-enabled mode is due to its flexibility for WSN applications as compared to the non-beacon enabled mode. Our analysis is based on an accurate simulation model of the slotted CSMA/CA mechanism on top of a realistic physical layer, with respect to the IEEE 802.15.4 standard specification. The performance of the slotted CSMA/CA is evaluated and analyzed for different network settings to understand the impact of the protocol attributes (superframe order, beacon order and backoff exponent) on the network performance, namely in terms of throughput (S), average delay (D) and probability of success (Ps). We introduce the concept of utility (U) as a combination of two or more metrics, to determine the best offered load range for an optimal behavior of the network. We show that the optimal network performance using slotted CSMA/CA occurs in the range of 35% to 60% with respect to an utility function proportional to the network throughput (S) divided by the average delay (D).

On the performance limits of slotted CSMA/CA in IEEE 802.15.4 for broadcast transmissions in wireless sensor networks

The IEEE 802.15.4 has been adopted as a communication protocol standard for Low-Rate Wireless Private Area Networks (LRWPANs). While it appears as a promising candidate solution for Wireless Sensor Networks (WSNs), its adequacy must be carefully evaluated. In this paper, we analyze the performance limits of the slotted CSMA/CA medium access control (MAC) mechanism in the beacon-enabled mode for broadcast transmissions in WSNs. The motivation for evaluating the beacon-enabled mode is due to its flexibility and potential for WSN applications as compared to the non-beacon enabled mode. Our analysis is based on an accurate simulation model of the slotted CSMA/CA mechanism on top of a realistic physical layer, with respect to the IEEE 802.15.4 standard specification. The performance of the slotted CSMA/CA is evaluated and analyzed for different network settings to understand the impact of the protocol attributes (superframe order, beacon order and backoff exponent), the number of nodes and the data frame size on the network performance, namely in terms of throughput (S), average delay (D) and probability of success (Ps). We also analytically evaluate the impact of the slotted CSMA/CA overheads on the saturation throughput. We introduce the concept of utility (U) as a combination of two or more metrics, to determine the best offered load range for an optimal behavior of the network. We show that the optimal network performance using slotted CSMA/CA occurs in the range of 35% to 60% with respect to an utility function proportional to the network throughput (S) divided by the average delay (D).

Portfolio optimization with options

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Three essays on the psychology of investment and financial markets

Préface My thesis consists of three essays where I consider equilibrium asset prices and investment strategies when the market is likely to experience crashes and possibly sharp windfalls. Although each part is written as an independent and self contained article, the papers share a common behavioral approach in representing investors preferences regarding to extremal returns. Investors utility is defined over their relative performance rather than over their final wealth position, a method first proposed by Markowitz (1952b) and by Kahneman and Tversky (1979), that I extend to incorporate preferences over extremal outcomes. With the failure of the traditional expected utility models in reproducing the observed stylized features of financial markets, the Prospect theory of Kahneman and Tversky (1979) offered the first significant alternative to the expected utility paradigm by considering that people focus on gains and losses rather than on final positions. Under this setting, Barberis, Huang, and Santos (2000) and McQueen and Vorkink (2004) were able to build a representative agent optimization model which solution reproduced some of the observed risk premium and excess volatility. The research in behavioral finance is relatively new and its potential still to explore. The three essays composing my thesis propose to use and extend this setting to study investors behavior and investment strategies in a market where crashes and sharp windfalls are likely to occur. In the first paper, the preferences of a representative agent, relative to time varying positive and negative extremal thresholds are modelled and estimated. A new utility function that conciliates between expected utility maximization and tail-related performance measures is proposed. The model estimation shows that the representative agent preferences reveals a significant level of crash aversion and lottery-pursuit. Assuming a single risky asset economy the proposed specification is able to reproduce some of the distributional features exhibited by financial return series. The second part proposes and illustrates a preference-based asset allocation model taking into account investors crash aversion. Using the skewed t distribution, optimal allocations are characterized as a resulting tradeoff between the distribution four moments. The specification highlights the preference for odd moments and the aversion for even moments. Qualitatively, optimal portfolios are analyzed in terms of firm characteristics and in a setting that reflects real-time asset allocation, a systematic over-performance is obtained compared to the aggregate stock market. Finally, in my third article, dynamic option-based investment strategies are derived and illustrated for investors presenting downside loss aversion. The problem is solved in closed form when the stock market exhibits stochastic volatility and jumps. The specification of downside loss averse utility functions allows corresponding terminal wealth profiles to be expressed as options on the stochastic discount factor contingent on the loss aversion level. Therefore dynamic strategies reduce to the replicating portfolio using exchange traded and well selected options, and the risky stock.

Rebound Effects from Increased Efficiency in the Use of Energy by UK Households

In this paper, we use CGE modelling techniques to identify the impact on energy use of an improvement in energy efficiency in the household sector. The main findings are that 1) when the price of energy is measured in natural units, the increase in efficiency yields only to a modification of tastes, changing as a result, the composition of household consumption; 2) when households internalize efficiency, the improvement in energy efficiency reduces the price of energy in efficiency units, providing a source of improved competitiveness as the nominal wage and the price level both fall; 3) the short-run rebound can be greater than the long run rebound if the household demand elasticity is the same for both time frames, however, the short run rebound is always lower than in the long-run if the demand for energy is relatively more elastic in the long-run; 4) the introduction of habit formation changes the composition of household consumption, modifying the magnitude of the household rebound only in the short-run. In this period, household and economy wide rebound are lowest for external habit formation and highest when consumers’ preferences are defined using a conventional utility function.

No Good Deals - No Bad Models

Faced with the problem of pricing complex contingent claims, an investor seeks to make his valuations robust to model uncertainty. We construct a notion of a model- uncertainty-induced utility function and show that model uncertainty increases the investor's eff ective risk aversion. Using the model-uncertainty-induced utility function, we extend the \No Good Deals" methodology of Cochrane and Sa a-Requejo [2000] to compute lower and upper good deal bounds in the presence of model uncertainty. We illustrate the methodology using some numerical examples.