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Paradox has been an instrument to challenge the traditional expected utility theory. Paradox arises from the inconsistency between the empirical or experimental results and the theoretical deductions. In the expected utility theory field, there are many paradoxes or effects showing behaviors that are contradictory to the “theoretical” ones. Many studies questioned the validity of the expected utility theory by means of these paradoxes; while many others disqualified the expected utility theory as a descriptive model for human decision making behaviors. Among these paradoxes or effects, the Allais Paradox raised by Allais in 1953 is the most famous one.

This chapter explains how economic analysis can contribute to the delineation of the lone wolf’s opportunities and choices in a manner that allows operationally relevant advice to be contributed to the investigative process.

Using a risk-reward analytical framework we examine the lone wolf’s attack method opportunities and choices and identify those attack methods that would be chosen by lone wolves with different levels of risk aversion. We also use prospect theory as an alternative methodology for the determination of the lone wolf’s preference orderings over the available attack methods in a context where he references his actions against those of a predecessor whom he wishes to emulate.

We find that lone wolf terrorists with different levels of risk aversion can be expected to choose different attack methods or combinations of attack methods. More risk averse lone wolf terrorists will choose attack methods such as assassination. Less risk averse lone wolf terrorists will choose attack methods such as bombing, hostage-taking and unconventional attacks. Also, we find that lone wolf terrorists who reference their actions against ‘predecessor’ lone wolf terrorists will choose differently from among the available attack methods depending on which predecessor lone wolf is being referenced.

The analysis provides two different perspectives on terrorist choice but by no means exhausts the analytical alternatives. The analysis focuses on the fatalities and injuries inflicted whereas other perspectives might include different ‘payoffs’ series, including news or media coverage.

The chapter contributes an analysis of the order in which lone wolf terrorists with particular characteristics will choose from a set of available attack methods. During the course of our discussion we point out the consistency between the ‘rise’ of the lone wolf terrorist and the diseconomies to scale that are evident within the terrorism context. This presents the opportunity for new debates.

Optimal ordering decision for a retailer in a dual-sourcing procurement is an important research area. The main purpose of this paper is to explore a loss-averse retailer’s ordering decision in a dual-sourcing problem.

For a loss-averse retailer, the study obtains the optimal ordering decision to maximize expected utility. Based on sensitivity analysis, the properties of the optimal ordering decision are well discussed.

Under the optimal ordering quantity that maximizes expected loss aversion utility, the relevant expected profit of a retailer turns to be smaller under a bigger loss aversion coefficient. For this point, a retailer needs to balance between expected loss aversion utility maximization and expected profit maximization in deciding the optimal ordering policy in a dual-sourcing problem.

This paper reveals the influence of loss aversion on a retailer’s ordering decision in a dual-sourcing problem. Managerial insights are suggested to devise the optimal ordering policy for retailers in practice.

This work examines the joint pricing and ordering (JPO) decisions for a loss-averse retailer with quantity-oriented reference point (RP) effect under demand uncertainty.

The demand is assumed to be uncertain with the mean and variance as the only known information. The prospect theory is used to model the retailer's expected utility. An expected utility maximization model in the distribution-free approach (DFA) is then developed. Using duality theory, the expected utility under the worst-case distribution is transformed into tractable piece-wise functions. To examine the effectiveness of the DFA in coping with the demand uncertainty, a stochastic programming model is developed and its solutions are used as benchmarks.

The proposed model and solution approach can effectively hedge against the demand uncertainty. The JPO decisions are significantly influenced by the LA coefficient and the reference level. The LA has a stronger influence than the reference level does on the expected utility. An excessive LA is detrimental while an appropriate reference level is beneficial to the retailer.

The results of this work are applicable to loss-averse retailers with the quantity-oriented RP when making JPO decisions with difficulty in predicting the demands.

The demand is assumed to be uncertain in this work, but a certain demand distribution is usually assumed in the existing literature. The DFA is used to study JPO decisions for the loss-averse retailer with quantity-oriented RP effect under the uncertain demand.

We review the experimental evidence on risk aversion in controlled laboratory settings. We review the strengths and weaknesses of alternative elicitation procedures, the strengths and weaknesses of alternative estimation procedures, and finally the effect of controlling for risk attitudes on inferences in experiments.

The authors consider the mutual benefits of the ceding company and reinsurance company in the design of reinsurance contracts. Two objective functions to maximize social expected utilities are established, which are to maximize the sum of the expected utilities of both the ceding company and reinsurance company, and to maximize their products. The first objective function, additive, emphasizes the total gains of both parties, while the second, multiplicative, accounts for the degree of substitution of gains of one party through the loss of the other party. The optimal price and retention of reinsurance are found by a grid search method, and numerical analysis is conducted. The results indicate that the optimal solutions for two objective functions are quite different. However, optimal solutions are sensitive to the change of the means and volatilities of the claim loss for both objective functions. The results are potentially valuable to insurance regulators and government entities acting as reinsurers of last resort.

In this paper, the authors apply relatively simple, but in the view significant, methods and models to discuss the optimization of excess loss reinsurance strategy. The authors only consider the influence of loss distribution on optimal retention and reinsurance price but neglect the investment factor. The authors also consider the benefits of both ceding company and reinsurance company to determine optimal premium and retention of reinsurance jointly based on maximizing social utility: the sum (or the product) of expected utilities of reinsurance company and ceding company. The authors solve for optimal solutions numerically, applying simulation.

This paper establishes two optimization models of excess-of-loss reinsurance contract against catastrophic losses to determine optimal premium and retention. One model considers the sum of the expected utilities of a ceding company and a reinsurance company's expected utility; another considers the product of them. With an example, the authors find the optimal solutions of premium and retention of excess loss reinsurance. Finally, the authors carry out the sensitivity analysis. The results show that increasing the means and the volatilities of claim loss will increase the optimal retention and premium. For objective function I, increasing the coefficients of risk aversion of or reducing the coefficients of risk aversion of will make the optimal retention reduced but the optimal premium increased, and vice versa. However, for objective function 2, the change of coefficient of risk aversion has no effect on optimal solutions.

Utility of the two partners: The ceding company and the reinsurance company, may have different weights and different significance. The authors have not studied their relative significance. The simulation approach in numerical methods limits us to the probability distributions and stochastic processes the authors use, based on, generally speaking, lognormal models of rates of return. This may need to be generalized to other returns, including possible models of shocks through jump processes.

In the recent two decades, reinsurance companies have played a great role in hedging mega-catastrophic losses. For example, reinsurance companies (and special loss sharing arrangements) paid as much as two-thirds of the insured losses for the September 11, 2001 tragedy. Furthermore, large catastrophic events have increased the role of governments and regulators as reinsurers of last resort. The authors hope that the authors provide guidance for possible balancing of the needs of two counterparties to reinsurance contracts.

Nearly all governments around the world are engaged in regulation of insurance and reinsurance, and some are reinsurers themselves. The authors provide guidance for them in these activities.

The authors believe this paper to be a completely new and original contribution in the area, by providing models for balancing the utility to the ceding insurance company and the reinsurance company.

我們探討分出公司和再保險公司在再保險合約的設計上、如何能達至互利互惠。研究確立了兩個目標函數，分別為把分出公司和再保險公司兩者之預期效用的總和最大化，以及把它們的產品最佳化。第一個目標函數是加法的，強調兩個參與方的總增益;而第二個目標函數則是乘法的，這個目標函數，闡釋參與方因另一方虧損而有所收益之取代度。再保險的最佳價格和自留額是利用網格搜索法找出的，數值分析也予以進行。研究結果顯示，兩個目標函數的最佳解決方案甚為不同。唯最佳解決方案會對就這兩個目標函數而言的追討損失的波動、以及其平均值之改變產生敏感反應。研究結果將會見其價值於作為在萬不得已的時候的再保險人的保險業規管機構和政府實體。

在這學術論文裡，我們採用了相對簡單、但我們認為是重要的方法和模型，來探討超額賠款再保險策略的優化課題。我們只考慮虧損分佈對最佳自留額和再保險價格的影響，而不去檢視投資因素。我們亦考慮對分出公司和再保險公司兩者的利益，來釐定最佳保費和再保險的自留額，而這兩者則共同建基於把社會效益最大化之上：再保險公司和分出公司的預期效益的總和 (或其積數) 。 我們採用類比模仿方法、來解決尋求在數字上最佳解決方案的問題。

本研究建立了就應對嚴重虧損而設的兩個超額賠款再保險合約的優化模型，來釐定最佳的保費和自留額。其中一個模型考慮了分出公司和再保險公司兩者各自的預期效益的總和。另外的一個模型則考慮了兩者的預期效益的積數。透過例子，我們找到了保費和超額虧損再保險自留額的最佳解決方案。最後，我們進行了敏感度分析。研究結果顯示、若增加追討損失的平均值和波動，則最佳自留額和保費也會隨之而增加。就第一個目標函數而言，若增加風險規避係數、或減少這個係數，則最佳自留額會隨之而減少，但最佳保費卻會隨之而增加，反之亦然。唯就第二個目標函數而言，風險規避係數的改變，對最佳解決方案是沒有影響的。

• – 有關的兩個夥伴之效用性：分出公司和再保險公司或有不同的份量和重要性。我們沒有探討兩者的相對重要性。

• – 我們以數值方法為核心的類比模仿研究法、使我們局限於機率分配和一般而言建基於投資報酬率對數常態模型之隨機過程的使用。我們或許需要調節研究法。以能概括其它回報收益，包括透過跳躍過程而可能達至之沖擊模型。

– 有關的兩個夥伴之效用性：分出公司和再保險公司或有不同的份量和重要性。我們沒有探討兩者的相對重要性。

– 我們以數值方法為核心的類比模仿研究法、使我們局限於機率分配和一般而言建基於投資報酬率對數常態模型之隨機過程的使用。我們或許需要調節研究法。以能概括其它回報收益，包括透過跳躍過程而可能達至之沖擊模型。

在過去20年裡，再保險公司在控制極嚴重災難性的損失上曾扮演重要的角色。例如、再保險公司 (以及特殊的損失分擔安排) 為了2001年9月11日的災難事件而支付多至保險損失的三分之二的費用。而且，重大的災難性事件使政府及作為最後出路再保險人的調控者得扮演更重要的角色。我們希望研究結果能為再保險合約兩對手提供指導，以平衡雙方的需要。

全球差不多每個政府都參與保險和再保險的管理工作，有部份更加本身就是再保險人。研究結果為他們的管理工作提供了指導。

我們相信本學術論文、提供了平衡分出保險公司和再保險公司效用性的模型，就此而言，本論文在相關的領域上作出了全新和獨創性的貢獻。

High levels of turnover in financial markets are consistent with the notion that trading, like gambling, yields direct utility to some agents. The purpose of this paper is to show that the presence of these agents attenuates covariance risk pricing and volatility, and implies a negative relation between volume and future returns. Since psychological literature indicates that the desirability of a gamble arises from the ex ante volatility of the outcome, the authors propose that agents derive greater utility from trading more volatile stocks. These stocks earn lower average returns in equilibrium, although the risk premium on the market portfolio is positive. The authors then consider a dynamic setting where agents’ utility from trading increases when they make positive profits in earlier rounds (e.g. due to an endowment effect). This leads to “bubbles,” i.e. disproportionate jumps in asset returns as a function of past prices, higher volume in up markets relative to down markets, as well as a leverage effect, wherein down markets are followed by higher volatility than up markets.

Analytical.

The presence of gamblers attenuates covariance risk pricing and volatility, and implies a negative relation between volume and future returns. If gamblers prefer more volatile stocks, these stocks earn lower average returns in equilibrium. If agents’ utility from trading increases when they make positive profits in earlier rounds (e.g. to an endowment effect), this leads to higher volume and lower volatility in up markets relative to down markets.

No paper has previously modeled agents who derive direct utility from trading.

The purpose of this paper is to examine the impact of renewable energy on the power supply chain and to study whether the renewable generator or the power grid that purchases power from the power spot market is better when the actual generation of renewable energy is insufficient. The authors want to compare and analyze the different power supply chain operation modes and discuss the optimal mode selection for renewable energy generator and power grid in different situations.

This paper studies the grid-led price competition game in the power supply chain, in which the power grid as a leader decides the price of transmission and distribution, and generators determine the power grid price. The renewable energy power generator and the traditional energy power generator conduct a price competition game; on the other hand, the power grid and power generators conduct Stackelberg games. The authors analyze the power supply of single power generator and two power generators, respectively, and research on the situation that the renewable energy cannot be fully recharged when the actual power generation is insufficient.

The study finds that both renewable and traditional power grid prices decline as price sensitivity coefficient of demand and installed capacity of renewable energy generators increase. Power grid premium decreases as the price sensitivity coefficient of demand increases, but rises as the installed capacity of renewable energy generator increases. When there is a shortage of power, if the installed capacity of renewable energy is relatively small and price sensitivity coefficient of demand is relatively large, the grid purchases the power from power spot market and shares cost with renewable energy generators, leading to higher expected profits of the renewable energy generators. On the contrary, the renewable energy generators prefer to make up power shortage themselves. For the power grid, purchasing the power by the renewable energy generators when there is a power shortage can bring more utility to the power grid when the installed capacity of renewable energy is lower and the demand price sensitivity coefficient is higher. When the installed capacity of renewable energy is high and the price sensitivity coefficient of demand is moderate, or the installed capacity of renewable energy is moderate and the demand price sensitivity coefficient is high, a generator that simultaneously possesses two kinds of energy source will bring more utility to the power grid. If the installed capacity of renewable energy and the demand price sensitivity coefficient both are small or the installed capacity of renewable energy and the price sensitivity coefficient of demand both are large, the power grid prefers to purchase the power by itself when there is a power shortage.

The goal of our paper analysis is to explore the implications of the theoretical model and address the series of research questions regarding the impact of the renewable energy on the power supply chain. The results of this study have key implications for reality. This paper sheds light on the power supply chain operation mode selection, which can potentially be used for the renewable energy generators to choose their operating mode and can also help traditional energy generators and power grid enterprises maximize their utility. This paper also has some references for the government to formulate the corresponding renewable energy development policy.

This paper studies the power operation mode under the uncertainty of supply and demand, and compares the advantages and disadvantages of renewable energy generator that makes up the shortage or the power grid purchases the power from power spot market then shares cost with the renewable energy generator. This paper analyzes the power grid-led coordination problem in a power supply chain, compares and analyzes the price competition game model of single power generator and dual power generators, and compares the different risk preferences of power grid.

This paper proposes and models stock loan lotteries, a financial innovation that improves individual investor welfare. Stock loan lotteries are prize-linked payoffs using securities lending fees.

This paper solves an existing theoretical model for an investor's utility-maximizing choices with and without stock loan lotteries and compares outcomes.

Stock loan lotteries motivate prospect theory investors to buy and hold risky assets with high expected returns. Stock loan lotteries improve welfare more for poor investors and improve welfare more in a model with market frictions such as trading costs.

Stock loan lotteries increase household savings, leading to greater financial wealth and security in retirement.

This paper proposes a new financial product that improves financial outcomes for individual investors.