Optimal payoffs under state-dependent preferences

Most decision theories, including expected utility theory, rank-dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem.     

Adaptive planning and uncertainty resolution

The article discusses uncertainty resolution and the approaches to uncertainty in planning. Statically perceived uncertainty may be described more or less explicitly in decision making. Stating various possible outcomes and, possibly, their numerical probabilities may allow quantitative theory to be applied. However, there will be a residual of genuine uncertainty due to the limits set by the available information. By “buying” more information the decision maker can decrease the genuine uncertainty. It is also often possible to reduce uncertainty by waiting. The most effective way is to state the expectations explicitly and to let the various future states of information correspond to alternative decisions in a conditional strategy. This requires a new kind of forecast that refers to the development of information available. A less efficient mode of planning can still take into consideration the fact that revisions are expected. This is flexible planning in a wide sense.     

Non-proportional reinsurance with risk preferences

The article on hand presents two complementary decision principles and their application to the non-proportional reinsurance business. Thereby these decision principles use a convex combination of risk measures and therefore allow the modelling of risk preferences of decision makers. In this regard, the main objective is to prove the risk preferences for this decision principles as well as to put them in the context of the decision theory. In this connection, the expected utility theory and the dual utility theory are explored. Furthermore the aspect of coherent risk measures is analyzed. Moreover for the two reinsurance models the special case of a fair reinsurance deductible on the one hand and the special case of a CVaR-decision maker on the other hand is examined.     

Tax Evasion and Equity Theory: An Investigative Approach

Traditional economic theory assumes rational individuals with stable preferences who, given an array of options and probabilities, maximize their expected utility. However, experimental research finds that individuals make systematic mistakes when attempting to maximize their expected utility. The economic psychology approach includes aspects of the traditional economic approach and the psychological approach that emphasizes values, attitudes, norms, conformity and morals.This paper investigates equity theory and tax evasion using the framework of prospect theory pioneered by Tversky and Kahneman. We design an investigation to identify if individual behavior follows the usual results of prospect theory, given a scenario that frames a perception of inequity. The investigation frames a scenario to invoke a controlled tax regime. The frame varies according to which inequity is being measured, exchange or social. Once the scenario is established, a questionnaire is designed to determine how the individual responds when filing taxes. The responses to the control questions are consistent with prospect theory. However, in general the responses to the framed questions, depicting inequity, are more consistent with expected utility theory.     

Background Risk, Demand for Insurance, and Choquet Expected Utility Preferences

This article deals with demand for insurance with a background risk in a nonprobabilized uncertainty framework, where preferences are represented by a nonadditive model of decision making. The Choquet expected utility model that we use generalizes expected utility and allows for a separation of the attitude towards uncertainty and the attitude towards wealth. When the insurable and the background risk are comonotone, the impact of the background risk on the demand for insurance is related to the attitude towards wealth. In contrast, when the two risks are anticomonotone, the attitude towards uncertainty is determinant. In this case, some of the resulting behaviors cannot be explained by the standard expected utility model.     

Pricing insurance and warranties: Ambiguity and correlated risks

This paper reports on the results of a questionnaire study of pricing decisions made by professional actuaries when the probabilities of a loss are either ambiguous or nonambiguous. Theoretical hypotheses derived from the expected utility model were compared with the implications of procedures described by practicing actuaries. Actuaries were asked to act as consultants to a computer manufacturer concerning the price of a warranty. The suggested prices were considerably higher when probabilities were ambiguous than when they were well-specified. These pricing decisions were consistent with the procedures described by actuaries but inconsistent with predictions from expected utility theory when the risks are perfectly correlated. Further insight into the actual decision process is provided by interviews with actuaries and an analysis of comments written on the questionnaire forms.     

Ambiguity aversion and the absence of wage indexation

This paper analyzes optimal wage contracting assuming agents are not subjective expected utility maximizers but are, instead, ambiguity (or uncertainty) averse decision makers who maximize Choquet expected utility. We show that such agents will choose not to include any indexation coverage in their wage contracts even when inflation is uncertain, unless the perceived inflation uncertainty is high enough. Significantly, the exercise does not presume any exogenous costs (e.g., transactions costs) of including indexation links.     

Reward–risk portfolio selection and stochastic dominance

The portfolio selection problem is traditionally modelled by two different approaches. The first one is based on an axiomatic model of risk-averse preferences, where decision makers are assumed to possess a utility function and the portfolio choice consists in maximizing the expected utility over the set of feasible portfolios. The second approach, first proposed by Markowitz is very intuitive and reduces the portfolio choice to a set of two criteria, reward and risk, with possible tradeoff analysis. Usually the reward–risk model is not consistent with the first approach, even when the decision is independent from the specific form of the risk-averse expected utility function, i.e. when one investment dominates another one by second-order stochastic dominance. In this paper we generalize the reward–risk model for portfolio selection. We define reward measures and risk measures by giving a set of properties these measures should satisfy. One of these properties will be the consistency with second-order stochastic dominance, to obtain a link with the expected utility portfolio selection. We characterize reward and risk measures and we discuss the implication for portfolio selection.     

Co-monotonicity of optimal investments and the design of structured financial products

We prove that, under very weak conditions, optimal financial products on complete markets are co-monotone with the reversed state price density. Optimality is meant in the sense of the maximization of an arbitrary preference model, e.g., expected utility theory or prospect theory. The proof is based on a result from transport theory. We apply the general result to specific situations, in particular the case of a market described by the Capital Asset Pricing Model or the Black–Scholes model, where we derive a generalization of the two-fund-separation theorem and give an extension to APT factor models and structured products with several underlyings. We use our results to derive a new approach to optimization in wealth management, based on a direct optimization of the return distribution of the portfolio. In particular, we show that optimal products can (essentially) be written as monotonic functions of the market return. We provide existence and nonexistence results for optimal products in this framework. Finally we apply our results to the study of bonus certificates, show that they are not optimal, and construct a cheaper product yielding the same return distribution.     

An evasive topic: theorizing about the hidden economy

This paper reviews some central issues that arise in theorizing about tax evasion decisions and the hidden economy. It starts from the Allingham and Sandmo (J. Public Econ. 1:323–338, 1972) modeling of the tax evasion decision as a choice under uncertainty based on expected utility maximization and risk aversion. It goes on to discuss alternative specifications of the taxpayer’s preferences with particular regard to the explanation of the extensive margin, i.e. the decision on whether or not to engage in tax evasion. It extends the model to the case of variable labor supply with work in both official and black labor markets. It then considers the application of the theory to taxes on wealth and income from capital, indirect tax evasion, and smuggling. It also includes a consideration of general equilibrium effects and of the problems that evasion causes for the theory of optimal income and commodity taxes. It concludes with a brief discussion of the implications of tax evasion for economic policy in the welfare state.     

Comparative statics and portfolio choices under the phantom decision model

This study characterizes attitudes toward uncertainty in the phantom decision model introduced by Izhakian and Izhakian (2015) and conducts a comparative statics analysis to examine how changes in phantom uncertainty and phantom aversion affect portfolio choices. First, “phantom averse” and “more phantom-averse” are defined in a manner that differs from Izhakian and Izhakian (2015). Assuming that utility functions have realization forms, the above notions are characterized by the shapes of their reduction components. For the portfolio choice problem that consists of one safe asset and one phantom asset, we derive sufficient conditions under which changes in phantom uncertainty and phantom aversion monotonically decrease the investment in the phantom asset. Some familiar concepts in expected utility theory are extended to the framework of the phantom decision model.     

Retail banking and behavioral financial engineering: The case of structured products

We apply cumulative prospect theory and hedonic framing to evaluate discount reverse convertibles (DRCs) and reverse convertible bonds (RCBs) as important examples of structured products from a boundedly rational investor’s point of view. While common expected utility theory would also conclude that DRCs and RCBs are of interest to investors with moderate return expectations and underestimated stock return volatility, that theory would overestimate the market success of DRCs and underestimate that of RCBs in comparison to a situation with bounded rationality. Hedonic framing and relatively low subjectively felt competence levels of investors are decisive for the demand for RCBs.     

从前景理论看纳税遵从决策与征管策略选择

本文认为,以理性和自利为假设前提的预期效用理论虽然可以解释一般的纳税遵从决策,却无法解释那些并不完全理性、自利的遵从行为,20世纪80年代以来前景理论的引入弥补了这方面的不足。前景理论的反射性效应、确定性效应和分离性效应原理解释了纳税人的实际决策与理性决策相偏离的现象,为税收征管策略的选择提供了重要的理论基础和政策启示。     

Risk-Adjusted Economic Value Analysis

Abstract

The ability of commonly used profitability measures to reflect risk exposure appropriately is evaluated and found lacking. As an alternative, a modern portfolio theory approach, based on utility theory, is recommended. Generalized formulas for calculating risk-adjusted economic values by deriving risk adjustments from certainty equivalents are developed by using the Markowitz expected utility maxim. Practical applications are described. Where appropriate, simplifying assumptions are shown to result in closed-form solutions, thereby reducing the need for extensive, stochastic cashflow simulations. The resulting formulas can be used to measure financial performance on a risk-adjusted basis consistently across different lines of business or to evaluate risk exposures in strategic alternatives.     

Simulating and Forecasting Utility Stock Returns: Arbitrage Pricing Theory vs. Capital Asset Pricing Model

Just when the capital asset pricing model (CAPM) has become accepted by public utility regulators as a method for estimating a utility's screening rate, academic criticism of the model's theoretical and empirical shortcomings has led to empirical testing of the alternative arbitrage pricing theory (APT). This paper expands on recent APT-CAPM performance comparisons by simulating returns of public utility stocks using versions of both models, as was done by Bower, Bower, and Logue in a 1984 paper. In addition, the models are used for ex-post forecasting of returns in a subsequent time period. The Litzenberger-Ramaswamy method is used to correct for errors-in-variables in the CAPM cross-sectional equation. This allows for estimating the security market line using firm betas. The same methodology is used in the APT stages. Three different criteria—the Theil inequality, the sources of mean square error, and Chen's estimated weights of expected return-are used to compare CAPM and APT simulation and forecasting of the equity screening rates. Tested on a sample of 128 public utility companies, results show that neither model is clearly dominant. There is a tendency for reversal of performance. The model that is superior for simulating returns tends to be inferior for forecasting them, and vice-versa.     

基于计算实验金融方法的决策偏好比较研究

风险决策偏好表征着个体在面对不确定条件或具有风险时的决策态度,不同的偏好特征以效用函数为载体,外在地表现为个体具体所运用的投资策略。风险决策机制的深入理解以及基于不同决策偏好的策略比较分析对投资者的投资决策具有重要意义。通过运用计算实验金融方法对传统决策偏好以及前景理论进行多角度的比较分析,研究发现基于前景理论构造的投资策略相比传统决策偏好具有较大的优势,对于投资者本身来说是一个最佳的策略选择。