Understanding Expected Utility for Decision Making

In this paper,we present a brief version of de Finetti-Ramsey’s subjective probability theory and provide a rigorous yet intuitively plausible explanation of expected utility using elementary mathematics.In a final section,we take up the case of some“Paradoxes in Expected Utility Theory”and try to reconcile them with the help of subjective probabilities.

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiple- priors utility and the technique of backward stochastic differential equations （BSDEs）, we transform the （^-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor＇s uncertainty. Our model investi- gates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flex- ibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.

On Utility Maximization with Random Interval Payoffs

This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets' prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.

Analysis of Optimal Portfolio with Different Utility Function

The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure （martingale measure） if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.

Some Likelihood Based Properties in Large Samples: Utility and Risk Aversion, Second Order Prior Selection and Posterior Density Stability

The likelihood function plays a central role in statistical analysis in relation to information, from both frequentist and Bayesian perspectives. In large samples several new properties of the likelihood in relation to information are developed here. The Arrow-Pratt absolute risk aversion measure is shown to be related to the Cramer-Rao Information bound. The derivative of the log-likelihood function is seen to provide a measure of information related stability for the Bayesian posterior density. As well, information similar prior densities can be defined reflecting the central role of likelihood in the Bayes learning paradigm.

Fuzzy-Bayes Decision Making with Reserved Judgement

This paper discusses a method for identifying states in a multistage Decision Making Problem in which an Indifferent Event is either predetermined or can be automatically derived after the fact. First, when they are pre-set, the amount of possible information about Indifferent Event tends to be large. Therefore, since the decision is risk tolerant, the Max-Product method of Tanaka et al. is used to calculate the expected utility possibility. Next, in the case of automatic derivation after the fact, the amount of information on the possibility of Indifferent Event is relatively small, so the expected utility possibility is derived using Zadeh’s Fuzzy Event Possibility Measure. Here, it is assumed that the setting of the utility function is independent of the information on the occurrence of the Indifferent Event and is identified by the decision maker by lot drawing using the certainty equivalence method. As a concrete example, we focus on the pass/fail decision of a recommendation test, which is a two choice question in the No-Data Problem, and illustrate the multistage state identification method. .

Optimal Risk Sharing for Maxmin Choquet Expected Utility Model

This article analyzes the Pareto optimal allocations,agreeable trades and agreeable bets under the maxmin Choquet expected utility(MCEU)model.We provide several useful characterizations for Pareto optimal allocations for risk averse agents.We derive the formulation descriptions for non-existence agreeable trades or agreeable bets for risk neutral agents.We build some relationships between ex-ante stage and interim stage on agreeable trades or bets when new information arrives.

Is the crop insurance program effective in China? Evidence from farmers analysis in five provinces

This paper aims to evaluate the effectiveness of the Chinese crop insurance program in terms of farmers＇ utility and welfare. A simulation model based on the power utility function was first developed to evaluate the effectiveness of crop insurance. Then, the Monte Carlo approach was used to generate the datasets of area, price, yield, cost, and income based on the characteristics of representative farmers, which were clustered and calibrated using the farm-level data of 574 individual farmers from five Chinese provinces. Finally, the effectiveness of Chinese crop insurance was evaluated by comparing the certainty equivalence（CE） of farmers＇ utility/welfare under alternative crop insurance scenarios. Government subsidy is a necessary premise for implementing the crop insurance program. The government should subsidize more than 50% of the crop insurance premium to motivate more farmers to participate in the program. The findings also show that the current crop insurance program in China has increased the farmers＇ welfare but still need to be improved to achieve the Pareto improvement and to make full use of the financial fund of the government. This paper is believed to not only extend academic research but also has significant implications for policymakers, especially in the context of rapid development of Chinese crop insurance with much issues such as rate, subsidy and coverage level needed to be improved.

On Fair Prices of a Contingent Claim with Random Interval Payoff

In order to get the price of a contingent claim with random interval payoff, a concept of fair price was proposed based on weighted expected utility maximization. After setting up a programming model of maximizing the weighted expected utility involving basic securities and contingent claim,and using techniques in optimization analysis,explicit expressions of the fair price interval for a contingent claim were derived. Relations between acceptable price interval and fair price interval were discussed. It is shown that all fair prices fit the demand for acceptability of a market.

Design of Principal-agent Incentive Mechanism between Government and NPO

Based on principal-agent theory,this paper establishes an incentive contract mechanism between government and NPO under asymmetric information,and analyzes the impact of absolute risk aversion and output level on the expected utility of government,NPO and society.Research shows that risk aversion is negatively correlated with the expected utility of government,NPO and society.The output coefficient is positively correlated with the expected utility of government,NPO and society.Reducing absolute risk aversion,increasing output coefficient and increasing government incentives can effectively motivate NPO to actively participate in social rescue activities.

Optimal liquidation with dynamic parameter updating: A forward approach

We propose a forward approach to study the performance of liquidation strategies under sequential model parameter updates.The forward liquidation program consists of pasting forward in time and in a time-consistent fashion a series of optimal liquidation problems.They are triggered at the parameter shift instances,thus entirely eliminating model error,and last at most till the next parameter update.However,due to the nature of the model dynamics,solutions may cease to exist in finite time,even before the subsequent parameter update.Furthermore,forward liquidation strategies may never lead to full liquidation,even though they maximize the average utility of revenue and always preserve time-consistency.In juxtaposition,the traditional approach delivers full liquidation at the sought horizon but encounters considerable model error,generates value erosion,and is time-inconsistent.

Existence of Arrow-Debreu Equilibrium with S-shaped Utility Function

This paper characterizes the optimal solution of subjective expected utility with S-shaped utility function, by using the prospect theory （PT）. We also prove the existence of Arrow-Debreu equilibrium.

Experimental Design of Measuring Soil-Water Characteristic Curve of Unsaturated Soil Using Bayesian Approach

Soil-water characteristic curve (SWCC) is significant to estimate the site-specific unsaturated soil properties (such as unsaturated shear strength and coefficient of permeability) for geotechnical analyses involving unsaturated soils. Determining SWCC can be achieved by fitting data points obtained according to the prescribed experimental scheme, which is specified by the number of measuring points and their corresponding values of the control variable. The number of measuring points is limited since direct measurement of SWCC is often costly and time-consuming. Based on the limited number of measuring points, the estimated SWCC is unavoidably associated with uncertainties, which depends on measurement data obtained from the prescribed experimental scheme. Therefore, it is essential to plan the experimental scheme so as to reduce the uncertainty in the estimated SWCC. This study presented a Bayesian approach, called OBEDO, for probabilistic experimental design optimization of measuring SWCC based on the prior knowledge and information of testing apparatus. The uncertainty in estimated SWCC is quantified and the optimal experimental scheme with the maximum expected utility is determined by Subset Simulation optimization (SSO) in candidate experimental scheme space. The proposed approach is illustrated using an experimental design example given prior knowledge and the information of testing apparatus and is verified based on a set of real loess SWCC data, which were used to generate random experimental schemes to mimic the arbitrary arrangement of measuring points during SWCC testing in practice. Results show that the arbitrary arrangement of measuring points of SWCC testing is hardly superior to the optimal scheme obtained from OBEDO in terms of the expected utility. The proposed OBEDO approach provides a rational tool to optimize the arrangement of measuring points of SWCC test so as to obtain SWCC measurement data with relatively high expected utility for uncertainty reduction.

Using behavioural economics to understand tax compliance

‘Behavioural economics’,or the application of methods and evidence from other social sciences to economics,has increased greatly in significance and use in the last two decades.In this paper,we discuss the basic elements of behavioural economics.We then assess the applications of behavioural economics to the analysis of tax compliance.Our central conclusion is that many,perhaps most,of the recent insights on what motivates tax compliance have flowed directly from behavioural economics.We conclude with suggestions on–and predictions of–directions in which future applications should prove useful.

NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.

A hierarchical analytical model for performance management of integrated logistics

In this paper,a holistic hierarchical analytical model is proposed to assess the performance of enablers in an integrated logistics system.Due to the ambiguous and complex environment,various refinements are needed to assess enablers and prioritize for the criteria such as economic,operational,and environment.The proposed hierarchical model is developed by a systematic approach that includes fuzzy analytical hierarchy process(FAHP),triangular fuzzy numbers(TFN),an evidential reasoning algorithm(ERA),and expected utility theory(EUT).The FAHP is used to analyze and obtain the weights of the criteria by considering the expert’s opinions.ERA is used to synthesize the enablers based on the selected criteria.These enablers are represented using subjective assessment along with a set of evaluation grades for a qualitative attribute.EUT helps in obtaining crisp values of enablers for their performance estimation.With these set of methodologies,a hierarchical model is proposed that prevent low flexibility and inadequate appropriateness of the proposed model.Further,the model helps in scenario generation for the logistics professionals who are facing various problems in integrating logistics and incorporating sustainability due to lack of appropriate methodologies and evaluation techniques.Finally,sensitivity analysis is used for overall model validation.

Risk and Potential:An Asset Allocation Framework with Applications to Robo-Advising

We propose a novel dynamic asset allocation framework based on a family of mean-variance-induced utility functions that alleviate the non-monotonicity and time-inconsistency problems of mean-variance optimization.The utility functions are motivated by the equivalence between the mean-variance objective and a quadratic utility function.Crucially,our framework differs from mean-variance analysis in that we allow different treatment of upside and downside deviations from a target wealth level.This naturally leads to a different characterization of possible investment outcomes below and above a target wealth as risk and potential.Our proposed asset allocation framework retains two attractive features of mean-variance optimization:an intuitive explanation of the investment objective and an easily computed optimal strategy.We establish a semi-analytical solution for the optimal trading strategy in our framework and provide numerical examples to illustrate its behavior.Finally,we discuss applications of this framework to robo-advisors.

Remarks on Equality of Two Distributions under Some Partial Orders

In this note we establish some appropriate conditions for stochastic equality of two random vari- ables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.

Crisis Stability and Transparency

The strategic relation between a few-nuclear state and a strong-nuclear state is studied in this paper. And a theorem about crisis stability and transparency of nuclear forces of few-nuclear state is proved in our model.

A Note on the Mean-Variance Criteria for Discrete Time Financial Markets

It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.