Certainty Equivalent Method Research Articles

Dynamic scaling-based immersion and invariance adaptive pose tracking control using dual quaternions

This paper investigates the position and attitude (pose) tracking control of a rigid body with uncertain mass and inertia. By virtue of the dual quaternion description, a six-degree-of-freedom (6-DOF) relative motion model is established in an integrated and compact way. Then an adaptive pose tracking controller is proposed based on the immersion and invariance (I&I) theory, where the key integrability obstacle is overcome by the dynamic scaling technique. Compared with the existing filter system-based method that constructs a filter system to circumvent the integrability obstacle, the dynamic scaling-based method is directly designed based on the original system, which is capable of retaining all benefits of the I&I design with much lower dimension dynamic extensions. Comparisons with the filter system-based I&I method and the classical certainty equivalent method are first carried out from the theoretical analyses, which elucidate benefits of the proposed method in lower control demands. Then the comparative simulations are conducted to verify the features and effectiveness of the proposed dynamic scaling-based I&I adaptive control scheme.

METHODS FOR ACCOUNTING FOR RISKS IN LONG-TERM PROJECTS

Risks represent a large portion of a project’s success. This is especially important in long-term projects such as public-private partnerships (PPPs) due to their complicated nature and long duration. Risks manifest in these projects throughout the project phases and can have severe effects on them. Previous literature has studied and reported on various methods for incorporating risks long-term projects; however, there is no universal method used. Hence, this paper identifies and reviews the most commonly used methods. Four methods were identified, which are risk adjusted discount rate, uncertain parameters method, certainty equivalent method, and decoupled net present value (NPV) method. These methods were discussed and contrasted in order to show their uses for long-term projects such as PPPs. The first method was found to incorporate both risk and time in a combined method while the other methods relied on decoupling of the risk and time due to their different natures.

Dairy farmers' risk attitudes and their perceptions towards environmental risks in Northwest Turkey

This study aims to determine the factors that affect dairy farmers' risk attitudes and their perceptions towards environmental risks in Northwest Turkey. By the proportional sampling method, data were collected from 381 dairy farmers. The survey was performed from September 2020 to June 2021. The study data were evaluated by descriptive statistics, risk matrix method, equally likely certainty equivalent method and probit model. In this study, severe storm, excessive rainfall/flood, livestock diseases, high temperature and drought was posed an important risk for dairy farmers. The majority of them showed risk aversion behaviour. Age, education level, household size, dairy farming experience, the number of dairy cattle, the land ownership status, livestock insurance and access of agricultural credits had a significant effect on risk perceptions and attitudes of dairy farmers. As a result, these findings are expected to ensure contribution to rural development, province and region economy, insurance institutions, agricultural policy makers, and further emphasizing the importance of environmental risks in dairy farming activity

A simple but powerful simulated certainty equivalent approximation method for dynamic stochastic problems

We introduce a novel simulated certainty equivalent approximation (SCEQ) method for solving dynamic stochastic problems. Our examples show that SCEQ can quickly solve high‐dimensional finite‐ or infinite‐horizon, stationary or nonstationary dynamic stochastic problems with hundreds of state variables, a wide state space, and occasionally binding constraints. With the SCEQ method, a desktop computer will suffice for large problems, but it can also use parallel tools efficiently. The SCEQ method is simple, stable, and can utilize any solver, making it suitable for solving complex economic problems that cannot be solved by other algorithms.

Intuitionistic fuzzy risk adjusted discount rate and certainty equivalent methods for risky projects

Risk adjusted interest rate (RADR) method and certainty equivalent (CE) method are the two popular methods used under risky conditions in the investment analysis. However, it should not be forgotten that there may be a vagueness in the estimation of risk factors. In this study, novel RADR and CE methods are extended for use under uncertainty by using single valued intuitionistic fuzzy (IF) sets. All investment parameters are used as IF parameters. High speed rail and nuclear power plant investments given in the study were analyzed with IF-RADR and IF-CE methods. This study constitutes an important resource on how to analyze investments under risk with other fuzzy sets extensions. Another important aspect of the study is that the paper determines IF numbers consciously instead of assigning random fuzzy numbers and letting them be applied, e.g., IF-RADR and IF-CE values are determined to express the same vagueness and impreciseness. The study also includes an IF sensitivity analysis for a nuclear power plant investment problem. It is concluded with discussions and future research suggestions.

Simulation-Based Business Valuation: Methodical Implementation in the Valuation Practice

The simulation-based company valuation values a company on the basis of the risks actually present in the company without having to derive them from the capital market data. The simulation-based company valuation takes into account the market imperfections, such as the probability of insolvency or the lack of diversification, and fulfils the legal requirements and auditing standards for a company valuation. The simulation-based company valuation is an alternative to the CAPM-based company valuation, which, under the assumption of perfect capital markets, derives the risks through capital market comparisons. A simulation-based business valuation has many advantages and is particularly suitable for valuing medium-sized companies, start-ups, companies in a crisis, and for integrating country-specific risks into business valuations. Due to the internationally widespread use of the CAPM, a simulation-based company valuation is still rarely used in practice. This article shows which valuation formulas are necessary for the application of a simulation-based company valuation. These are used for both the certainty equivalent method and for the risk premium method. In a concrete and valuation example, the simulation-based business planning and company valuation is carried out, and the derived valuation formulas are applied in a way that allows a transfer to concrete valuation cases in practice. It is shown that the certainty equivalent method and the risk premium method lead to identical company values.

Measuring the impact of risk on LCOE (levelized cost of energy) in geothermal technology

Geothermal technology has a high level of uncertainty and, thus, requires thorough risk analysis for economic decisions. The levelized cost of energy (LCOE) is a basic economic analysis widely used in determining an investment or energy mix. Many reputable institutions and government agencies provide LCOE, to which they apply different levels of discount rates to reflect project risk. To this end, the weighted average cost of capital (WACC) is frequently used as a proxy for project risk-adjusted discount rate. However, whether using a higher discount rate for a riskier project is appropriate in calculating LCOE has not been scrutinized. The purpose of this paper is to propose a certainty equivalent method of LCOE as an alternative way for considering risk. We present a theoretical background and formula based on the utility theory, improving the probabilistic LCOE estimation methodology of previous studies. We also perform scenario analysis to show how the certainty equivalent model changes LCOE reflecting different level of risk of the individual variables, which traditional LCOE does not. Additionally, we suggest that the traditional LCOE should be used prudently, recognizing it can distort the result when an individual project has a different level of risk from the industry average.

Surgical Scheduling with Constrained Patient Waiting Times

We consider a surgical case scheduling problem with the objective of minimizing the expected time span of the schedule subject to a prespecified upper bound on the expected waiting time for each patient. The problem is challenging due to its combinatorial and nonlinear nature, and we focus on developing approximate methods to solve the problem. Specifically, we study two approximation methods. In the certainty equivalent method, we approximate the expected time span of the cases by assuming that the waiting time of each surgical case is a deterministic value. In the variance bounding method, we approximate the expected time span based on upper bounds on the variance of the surgical case waiting times. We show that the certainty equivalent method leads to a lower bound on the optimal expected time span, while the variance bounding method leads to an upper bound. Both methods suggest a simple sequencing rule, which is to sort the surgical cases in the ascending order of the surgical duration variability. Based on the upper and lower bounds, we derive a closed‐form, distribution‐free relative error bound for our sequencing rule, and show that it is uniformly bounded with respect to the number of cases. We also conduct a case study based on real‐life data on hernia repair procedures at the Jewish General Hospital in Montréal, to demonstrate our analytical models and their potential benefits for improving surgical scheduling. Finally, we conclude the paper by mentioning a few future research directions.

Preference reversals during risk elicitation.

Understanding human behavior from the perspective of normative and descriptive theories depends on human agents having stable and coherent decision-making preferences. Both utility theory (expected rational behavior; von Neumann & Morgenstern, 1947) and prospect theory, with its certainty equivalent (CE) method (expected irrational behavior; Tversky & Kahneman, 1992), assume stable behavioral patterns of risk preferences. In contrast, our research pursues the opposite proposal: Human preferences (rational or irrational) are not stable; variations in the decision context during risk elicitation determine people's preferences even when the utilities of choice options are available. Accordingly, we found evidence that decision makers reverse their risk preferences between CE tasks with logarithmically spaced certainty (unequal number of risk-averse and risk-seeking sure options) and linearly spaced certainty (equal number of risk-averse and risk-seeking sure options). The results revealed that the effect of probability range (low and high) on preferences, predicted by prospect theory, is an artifact of the logarithmically spaced sure options. When the sure options were linearly spaced, the probability range no longer influenced risk preferences, indicating a preference reversal between decision tasks. Our findings highlight a need to investigate how the predictions of descriptive decision-making theories are shaped by their risk elicitation methods. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

Theory and practice of valuation approaches in renewable energy investments: a survey among investment professionals

This paper reports the results of a survey among Swiss and German investors in renewable energy (RE) - a challenging undertaking due to the restricted data access for those typically non-trade assets. The research's focus is placed on capital budgeting techniques, risk assessment, risk mitigation, cost of capital approaches, and risk-adjustment processes. The results are both reassuring and surprising. The majority of organisations still employ well-established discounted cash flow based techniques while other approaches propagated in finance theory, such as the certainty equivalent method, are seldom applied. A surprising number of organisations still use their firm's risk within discount rates in RE valuations instead of project risk. Beside of taking systematic risk into account in line with the capital asset pricing model, various diversifiable unsystematic risk components are considered in RE valuation. We also find clear evidence about materialised risk influencing personal risk preferences and some evidence about cultural differences in valuation.

Factors influencing hybrid maize farmers' risk attitudes and their perceptions in Punjab Province, Pakistan

Hybrid maize farmers have to face diverse kinds of climate, biological, price and financial risks. Farmers' risk perceptions and risk attitudes are essential elements influencing farm operations and management decisions. However, this important issue has been overlooked in the contemporary studies and therefore there is a dearth of literature on this important issue. The present research is therefore, an attempt to fill this gap. This study aims to quantify hybrid maize farmers' perceptions of disastrous risks, their attitudes towards risk and to explore the impacts of various farm and farm household factors on farmers' risk attitudes and risk perceptions. The present study is conducted in four hybrid maize growing districts of Punjab Province, Pakistan, using cross-sectional data of 400 hybrid maize farmers. Risk matrix and equally likely certainty equivalent (ELCE) method are used to rank farmers' perceptions of four catastrophic risk sources including climate, biological, price and financial risks and to investigate farmers' risk aversion attitudes, respectively. Furthermore, probit regression is used to analyze the determinants affecting farmers' risk attitudes and risk perceptions. The results of the study showed that majority of farmers are risk averse in nature and perceive price, biological and climate to be potential sources of risks to their farm enterprise. In addition, analysis divulges that distance from farm to main market, off-farm income, location dummies for Sahiwal and Okara, age, maize farming experience, access to extension agent, significantly (either negatively or positively) influence farmers' risk attitudes and risk perceptions. The study delivers valuable insights for farmers, agricultural insurance sector, extension services researchers and agricultural policy makers about the local understanding of risks to hybrid maize crop in developing countries, like Pakistan, and have implications for research on farmers' adaptation to exposed risks.

DOES GLOBAL SHAPES OF UTILITY FUNCTIONS MATTER FOR INVESTMENT DECISIONS?

ABSTRACTThe study investigates relation between global shapes of utility functions and investor preferences towards particular asset classes for investment decisions. Global shapes that emerge are fully concave, fully convex, Reverse‐S and S‐shaped utility functions, using the certainty equivalence method for eliciting risk preferences. Investor clusters show existence of two types of investors, preference towards financial assets (bank deposits, insurance, pension and provident fund, shares and mutual funds) vs traditional assets (chit funds, gold and precious metals, real estate, postal savings, and government bonds). Investors with reverse‐S and S‐shaped utility functions prefer investment in financial assets, while investors with fully concave and fully convex utility functions prefer traditional assets. Prior studies suggest reverse‐S and S‐shaped category of investors perceive risk in terms of gains and losses, and financial assets with ready price quotes facilitate such buying and selling. In contrast, fully concave and fully convex utility functions prefer investment in traditional assets that requires long term horizon and stable risk preferences. Among demographics, males with reverse‐S shaped utility function are more likely to invest in financial assets, and increase in dependents reduces the possibility to invest in financial assets.

A nonlinear certainty equivalent approximation method for dynamic stochastic problems

This paper introduces a nonlinear certainty‐equivalent approximation method for dynamic stochastic problems. We first introduce a novel, stable, and efficient method for computing the decision rules in deterministic dynamic economic problems. We use the results as nonlinear and global certainty‐equivalent approximations for solutions to stochastic problems, and compare their accuracy to the common linear and local certainty‐equivalent methods. Our examples demonstrate that this method can be applied to solve high‐dimensional problems with up to 400 state variables with acceptable accuracy. This method can also be applied to solve problems with inequality constraints. These features make the nonlinear certainty‐equivalent approximation method suitable for solving complex economic problems, where other algorithms, such as log‐linearization, fail to produce a valid global approximation or are far less tractable. New Keynesian DSGE model competitive equilibrium parallel computing sparse grid approximation real business cycle model C61 C63 C68 E31 E52

Why the risk-adjusted discount rate method is a better method than the certainty equivalent method: a teaching perspective

One of the more popular methods of risk analysis in capital budgeting is the certainty equivalent method. In this paper, we discuss the major drawbacks of using this method, and strongly argue in favour of the risk-adjusted discount rate method. The calculation of certainty equivalent factors, the use of risk-free rate as the discount rate, the reinvestment rate assumption and the practical problems for multinational corporations for using the certainty equivalent method are discussed. We also discuss the concept of cost of capital and its role in relation to the use of the two methods of risk analysis.

Why the risk-adjusted discount rate method is a better method than the certainty equivalent method: a teaching perspective

Why the risk-adjusted discount rate method is a better method than the certainty equivalent method: a teaching perspective

Bilateral learning model in construction claim negotiations

Purpose – The learning ability on critical bargaining information contributes to accelerating construction claim negotiations in the win-win situation. The purpose of this paper is to study how to apply Zeuthen strategy and Bayesian learning to simulate the dynamic bargaining process of claim negotiations with the consideration of discount factor and risk attitude. Design/methodology/approach – The authors first adopted certainty equivalent method and curve fitting to build a party’s own curve utility function. Taking the opponent’s bottom line as the learning goal, the authors introduced Bayesian learning to refine former predicted linear utility function of the opponent according to every new counteroffer. Both parties’ utility functions were revised by taking discount factors into consideration. Accordingly, the authors developed a bilateral learning model in construction claim negotiations based on Zeuthen strategy. Findings – The consistency of Zeuthen strategy and the Nash bargaining solution model guarantees the effectiveness of the bilateral learning model. Moreover, the illustrative example verifies the feasibility of this model. Research limitations/implications – As the authors developed the bilateral learning model by mathematical deduction, scholars are expected to collect empirical cases and compare actual solutions and model solutions in order to modify the model in future studies. Practical implications – Negotiators could refer to this model to make offers dynamically, which is favorable for the parties to reach an agreement quickly and to avoid the escalation of claims into disputes. Originality/value – The proposed model provides a supplement to the existing studies on dynamic construction claim negotiations.

An empirical assessment of farmers' risk attitudes in flood-prone areas of Pakistan

Farmers are confronted with several sources of climatic risks. As such, their risk attitudes play an important role in farm management decisions. Few studies have attempted to explore farmers' risk attitudes in flood-prone areas. This study examines the effects of socio-economic factors on risk attitudes of farmers in a flood-prone area of Pakistan. The data were collected from 168 subsistence farmers through a standardized questionnaire. The farmers were selected through multi-stage sampling techniques. For farmers' risk attitude measurement, Equally Likely Certainty Equivalent (ELCE) method and a cubic utility function were employed. Risk perceptions of farmers were measured by the risk matrix technique. A Logit model was employed to investigate the effects of socio-economic factors on farmers' risk attitudes. The findings of the study reveal that the majority of farmers were risk averse in nature. The results for the logit model show that education, experience, farmers' group, landholding size, off-farm income, and risk perceptions of floods significantly affect the risk attitude of farmers. The study provides useful insights into the most important factors affecting the risk attitude of farmers. The results have implications for policy makers in providing farmers with accurate risk mitigating and management tools, such as agricultural credit and crop insurance, to cope with climatic risks.

Equal Tails: A Simple Method to Elicit Utility Under Violations of Expected Utility

Classical methods to elicit utility are biased because most individuals do not treat probabilities linearly. We propose a simple modification of the classical methods that equates, for all prospects being compared, the range of outcomes. We argue that the modification should work in theory, and test the modification experimentally. Our first experiment confirms that the modified certainty equivalent method reduces the curvature of the S-shaped value function. The second experiment is a novel design that compares the trade-off method with the three classical methods in their original and modified forms. Our equal-tails modification of both the certainty equivalent and the lottery equivalent method produces results consistent with the trade-off method. The lottery equivalent modification is particularly useful to elicit utility points when outcomes are nonquantifiable.

Differences in cognitive control between real and hypothetical payoffs

This study focuses on the question of neural differences in the evaluation of hypothetical and real payoffs. Hypothetical payoffs are not incentive compatible and are, therefore, not considered to be reliable. Behavioral differences between the evaluation of hypothetical and real payoffs can be attributed to this incentive effect. Because real payoff mechanisms are not always applicable in the field, it is necessary to know in which way both types of payoffs affect evaluation processes. In order to delineate the cognitive processes related to hypothetical bias, we conducted a within-subject EEG experiment with hypothetical and real payoffs. A certainty equivalent elicitation method for measuring risk attitudes was performed in which subjects had to indicate whether they preferred playing a lottery or receiving a sure payoff instead. At the behavioral level, subjects were more risk averse for real payoff choices, confirming a hypothetical bias. EEG-derived event-related potentials provide evidence that the processes underlying these differences in evaluations differ. A higher N2 component for hypothetical payoffs revealed increased cognitive control for hypothetical decisions. These neuronal underpinnings indicate additional evaluation processes in hypothetical choice paradigms, which can explain the shift in risk attitude toward the expected value of a lottery.

Stability of probability effects in utility elicitation

The present study investigates the impact of probability levels on the response mode bias in utility elicitation and its stability across a wide range of conditions. Experiments are performed with subjects from two different cultures, Austria and Pakistan, and a variety of methods to measure risk attitudes of subjects on a cardinal scale are used. Results indicate robust influences of probability levels on both the Certainty Equivalent method and the Probability Equivalent method of utility elicitation. Both methods are affected by probability changes in the opposite direction, creating the characteristic “tailwhip” pattern observed in previous research. Our study shows that this effect remains stable across different cultural backgrounds, measurement methods, and problem parameters, and is thus not an artefact but a reproducible phenomenon.