Expected Utility Framework Research Articles

Rationalizing Present and Future Bias

This paper rationalizes both present and future bias in a single expected utility framework. The model considers a situation where mortality risk depends on the current state of health. When the state transition satisfies total positivity of order 2, rational decision makers are shown to have present bias when in poor health and future bias when in good health. The findings suggest that unhealthy behavior and resulting poor health may be the cause of present bias not its consequence as is often believed.

Efficient Retirement Financial Strategies

Today's retirees face the daunting task of determining appropriate investment and spending strategies for their accumulated savings. Financial economists have addressed their problem using an expected utility framework. In contrast, many financial advisors rely instead on rules of thumb. We show that some of the popular rules are inconsistent with expected utility maximization, since they subject retirees to avoidable, non-market risk. We also highlight the importance of earmarking - the existence of a one-to-one correspondence between investments and future spending - and show that a natural way to implement earmarking is to create a lockbox strategy.

Integrated Risk Management for Newsvendors with Value-at-Risk Constraints

We study a newsvendor problem with profit risk control using value-at-risk (VaR) constraints. When a firm’s demand correlates with the price of a tradable financial asset, both financial tools (derivatives) and operational tools (inventory) can be used for profit risk management. Such integrated risk management (IRM) approaches have been studied using various optimization frameworks to reflect the risk aversion of decision-makers. To the best of our knowledge, we are the first to study IRM in a newsvendor setting using profit maximization under VaR constraints. The VaR constraints allow for flexibility in the choice of profit target, [Formula: see text], and confidence level of achieving it, [Formula: see text]. It is important to understand the implications of different [Formula: see text] choices: some choices result in inventory decisions exhibiting risk aversion (and risk neutrality), whereas others result in inventory decisions exhibiting risk seeking. We demonstrate that without financial hedging, under the risk-averse [Formula: see text] choices, the decision-maker has to sacrifice mean profit for risk control by stocking below the profit-maximizing (or the risk-neutral) inventory level. When financial hedging is available, however, the decision-maker can use it alone to control the profit risk, even when demand only partially correlates with the price of the financial asset used. Thus, inventory is solely used for profit maximization, and financial hedging is solely used for profit control. This separation of inventory and financial hedging decisions simplifies the IRM implementation. Such simplification however, is not the case under the mean-variance or expected utility frameworks. In these risk-averse frameworks, both inventory and financial hedging must combine to control risk control, and, thus, these two types of decisions are often highly interdependent. VaR constraints, often preferred by regulators, may be helpful in implementing IRM in many regulated industrial settings.

A Risk Management Tool or an Investment Strategy? Understanding the Unstable Farm Insurance Demand via a Gain-Loss Framework

Risk management tools are at the core of farm policy in many developed countries, and their effectiveness relies on the appropriate mechanism design. This study developed a gain-loss framework based on prospect theory to examine the reasons for the declining use of the main risk management tool offered to farmers despite growing volatility in returns. Using the administrative Ontario Farm Income Database (OFID) 2003 to 2013 and taking the beef sector as the example, this study found that the gain-loss framework predicts and explains the dynamic program participation pattern better than the conventional expected utility framework. Farms were found to be more likely to stay enrolled in the program when they experienced either larger gains or losses in revenue compared to previous years, suggesting that they were using the insurance programs both as an investment strategy (to seek government subsidies) and as a risk management tool (to protect against business risks), though the effects of revenue losses and hence risk management needs were stronger than gains. In addition, the program payment history and farm characteristics also shape the dynamic participation patterns. The findings increased the understanding of the drivers of withdrawal behavior associated with government-sponsored business risk management programs.

On the Optimal Combination of Annuities and Tontines

Tontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines can be combined to form a retirement plan which is cheaper than an annuity, but provides a less volatile retirement income than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: The previously introduced tonuity, a product very similar to the tonuity which we call and a portfolio consisting of an annuity and a tontine. We show that the payoffs of a tonuity and an antine can be replicated by a portfolio consisting of an annuity and a tontine. Consequently, policyholders achieve higher expected utility levels when choosing the portfolio over the novel retirement products tonuity and antine. Further, we derive conditions on the premium loadings of annuities and tontines indicating when the optimal portfolio is investing a positive amount in both annuity and tontine, and when the optimal portfolio turns out to be a pure annuity or a pure tontine.

Alternative Approaches to Comparative nth-Degree Risk Aversion

This paper extends the three main approaches to comparative risk aversion—the risk premium approach and the probability premium approach of Pratt (1964) [Risk aversion in the small and in the large. Econometrica 32(1-2):122–136] and the comparative statics approach of Jindapon and Neilson (2007) [Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach. J. Econom. Theory 136(1):719–728]—to study comparative nth-degree risk aversion. These extensions can accommodate trading off an nth-degree risk increase and an mth-degree risk increase for any m, such that [Formula: see text]. It goes on to show that, in the expected utility framework, all of these general notions of comparative nth-degree risk aversion are equivalent and can be characterized by the concept of (n/m)th-degree Ross more risk aversion of Liu and Meyer (2013) [Substituting one risk increase for another: A method for measuring risk aversion. J. Econom. Theory 148(6):2706–2718]. This paper was accepted by Han Bleichrodt, decision analysis.

How much risk can you stomach? Individual differences in the tolerance of perceived risk across gender and risk domain

AbstractResearch within the psychological risk–return framework, namely, using the Domain‐Specific Risk‐Taking scale, has led to a conclusion that risk attitude—measured as an individual's sensitivity to the risk they perceive—is stable across people (e.g., gender) and domains (e.g., recreational, social, financial, & health). Risk taking differences across gender and domain have been interpreted in terms of differences in the magnitude of risk perceived (and expected benefit). Yet the Domain‐Specific Risk‐Taking scale items, contrived by researchers rather than decision makers themselves, may have failed to detect differences in perceived risk attitude by failing to adequately represent all combinations of risks and benefits across gender and domains. In Study 1, participants generated their own examples of activities, which we selected among in Studies 2 and 3 to construct a new scale representing various levels of perceived risk and expected benefit. Our findings reveal that women are more sensitive than men to risk they perceive (i.e., are less tolerant of risk) in the recreational, social, and financial domains but not in the health domain. Risk attitude also differed across domains, with participants tolerating more risk in some domains than in others. We conclude that gender and domain differences in risk taking stem partly from gender and domain differences in people's sensitivity to perceived risks. Our findings have theoretical implications for the psychological risk–return framework and bridge with other theoretical approaches, such as the expected utility framework. Our studies also provide a new scale for assessing differences in attitudes toward risk that overcomes shortcomings of existing scales.

Optimal Insurance Level Without the Expected-Utility Framework

Mossin's Theorem (full insurance with a fair premium and partial insurance with an unfair premium) is re-examined without the expected-utility paradigm where risk-aversion is defined in terms of mean-preserving spreads. Under the same assumption, two key results are known to hold for coinsurance: (1) Mossin's Theorem needs to be modified, and (2) the culprit for invalidating Mossin's Theorem is not the lack of an expected-utility framework, but a lack of sufficient ``smoothness'' of preferences in non-expected utility models. This article establishes that the first result holds for any constrained class of insurance contracts, and that the second result is not valid for deductible insurance and upper-limit insurance.

PCN143 HOW MUCH DO INDIVIDUALS VALUE ACCESS TO INNOVATIVE LUNG CANCER THERAPIES? A REVEALED PREFERENCE SURVEY OF HEALTHY ADULTS IN THE UNITED STATES (US)

To measure the value healthy individuals place on coverage of novel therapies that improve survival in the event they develop lung cancer. A recent web-based survey was administered to US adults without cancer to measure the incremental insurance premium respondents were willing to pay to access lung cancer therapies that improve survival. The survey used a ‘multiple random staircase revealed preference’ method to elicit willingness to pay—in terms of monthly premiums—for coverage of novel therapies associated with survival gains. Survival was calibrated based on a clinical trial comparing nivolumab to standard-of-care chemotherapy among patients with non-small cell lung cancer. Of 84,937 individuals invited via email, 1,191 responded and 163 completed the survey and met all eligibility criteria. The mean age of respondents was 50.0 (SD: 14.6) years, and 55.2% were female. On average, respondents were willing to pay an additional $57.00 (95% confidence interval (CI): $51.62-$62.37) monthly for coverage of novel therapy providing a 5-year survival of 15%, compared to standard-of-care therapy with a 5-year survival of 4%. Assuming risk neutrality, a lognormal survival distribution and annual lung cancer incidence of 0.07%, the mean survival gain conditional on being diagnosed with lung cancer is 1.95 years and the implied ex-ante value of a life-year under the expected utility framework is $500,066 (95% CI: $452,867-$547,177). Individuals place a higher value on insurance coverage for lung cancer treatments than previously estimated. Potential explanations may include: high valuations of life year gains for lung cancer and/or large risk premium individuals place on an insurance reducing future mortality risks.

Simultaneous Risk Aversion and Risk-Seeking Behavior in an Expected Utility Framework with Optimism

Simultaneous Risk Aversion and Risk-Seeking Behavior in an Expected Utility Framework with Optimism

Risk lovers, mixed risk loving and the preference to combine good with good

This paper examines the concept of 'risk loving' (that is risk seeking, intemperance, edginess, etc.), which can be characterised by preferences over simple lotteries. This paper analyses the notion of preferring to combine good with good, and bad with bad, as opposed to combining good with bad as usual. The significance of such preferences has implications on utility functions and are analysed in the paper. This paper extends Eeckhoudt and Schlesinger (2006) results to risk lovers, the results from Crainich et al. (2013) are also generalised to higher orders. We also generalise to higher orders the concept of bivariate risk seeking, introduced by Richard (1975) and called correlation loving by Epstein and Tanny (1980). In the expected utility framework, risk loving of order (N, M) coincides with the non-negativity of the (N, M)th partial derivative of the utility function. In dealing with mixed risk loving utility functions, we give several useful properties, for example, mixed risk loving is consistent with the mixture of positive exponential utilities and with non-increasing coefficients of absolute risk aversion at any order.

Optimal Retirement Products Under Money and Mortality Illusion

Many empirical studies confirm that policyholder's subjective mortality beliefs deviate from the information given by publicly available mortality tables. In this study, we look at the effect of subjective mortality beliefs on the perceived attractiveness of retirement products, focusing on two extreme products, conventional annuities (where the insurance company takes the longevity risk) and tontines (where a pool of policyholders shares the longevity risk). If risk loadings and charges are neglected, a standard expected utility framework, without subjective mortality beliefs, leads to conclude that annuities are always preferred to tontines (Yaari (1965), Milevsky and Salisbury (2015)). In the same setting, we show that this result is easily reversed if an individual perceives her peer's life expectancies to be lower than the ones used by the insurance company. We prove that, assuming such subjective beliefs, there exists a critical tontine pool size from which on the tontine is always preferred over the annuity. This suggests that tontines might be perceived as much more attractive than suggested by standard expected utility theory without subjective mortality beliefs.

The Annuity Puzzle: How Big is the Free Lunch Being Left on the Table?

The looming Savings Crisis is usually attributed to people either not saving enough or making poor investment choices, but we believe there's another culprit. Many investors could benefit from a 'free lunch' of pooling their longevity risk with others, but due to market inefficiencies, they do not. We quantify the size of this missed opportunity gap using an Expected Utility framework to compare self-managed savings versus the purchase of a zero-fee annuity.

Higher order risk attitudes and prevention under different timings of loss

This paper provides experimental evidence of the role of higher order risk attitudes—especially prudence—in prevention behavior. Prudence, under an expected utility framework, increases (decreases) self-protection effort compared to the risk neutral level when the risk of losing part of an income exists in a future (the same) period. Motivated by these predictions that give the exact test on prudence, an experiment was designed where subjects go through higher order risk attitude elicitation and make a self-protection decision. In contrast to the expected utility theory, the observed efforts are less than the risk neutral level, regardless of the timing of loss. This violation of expected utility predictions can be explained by probability weighting.

Strategies to manage hail risk in apple production

PurposeHail risk management is essential for successful farm management in German fruit production, particularly because hail events and associated losses have increased in recent years. The purpose of this paper is to conduct a detailed risk analysis comparing different strategies to manage hail risk, taking into account farmers’ risk aversion and farm-specific conditions.Design/methodology/approachWithin an expected utility framework, two different strategies for managing hail risk are compared: one belonging to the group of financial instruments (hail insurance) and the other to the group of technical instruments (anti-hail net). A unique data set comprising a ten-year time series of orchard-specific hail damage and hail insurance data is used.FindingsFor orchards with low local hail risk and low yield potential, not using hail risk mitigation is most efficient. For orchards with high local hail risk and high yield potential, anti-hail nets provide the highest certainty equivalents. For orchards with high local risk, but low yield potential, hail insurance is most efficient. For orchards, with low local risk, but high yield potential, the certainty equivalents are higher for anti-hail net, when the farmer is risk neutral or slightly risk-averse. With increasing risk aversion, hail insurance is most efficient, which can be explained by the greater degree of the instrument’s flexibility.Originality/valueThe novelty of the study lies in the direct comparison of the risk effects of anti-hail nets and hail insurance in fruit production.

Comparative precautionary saving under higher-order risk and recursive utility

Measuring and comparing the precautionary saving motive rest almost exclusively on the expected utility framework, and only focus on income risk or coefficients of the Arrow–Pratt type. We generalize the standard approach by characterizing comparative precautionary saving under recursive utility for increases in income risk and increases in risk on the saving return, including higher-order risk effects. We express the comparisons in terms of precautionary premia. In addition, we define a new class of preference coefficients, and derive the associated conditions to predict a stronger precautionary motive. The coefficients provide a detailed picture of the preferences sustaining precautionary saving and could be useful in applications.

Portfolio optimization under Solvency II

In the current low interest-rate and highly-regulated environment investing capital efficiently is one of the most important challenges insurance companies face. Certain quantitative parts of regulatory requirements (e.g. Solvency II capital requirements) result in constraints on the investment strategies. This paper mathematically describes the implications of Solvency II constraints on the investment strategies of insurance companies in an expected utility framework with a focus on the market risk module. For this constrained expected utility problem, we define a two-step approach that leads to closed-form approximations for the optimal investment strategies. This proposal circumvents the technical difficulties encountered when applying the convex duality approach or the theory of viscosity solutions. The investment strategies found using the two-step approach can be understood as the optimal investment strategies for constraint problems according to Solvency II. The impact of such constraints on the asset allocation and the performance of these strategies is assessed in a numerical case study.

Game-theoretic modeling of players’ ambiguities on external factors

We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players’ preferences on return-distribution vectors, essentially mappings from states of the world to distributions of returns to be received by players. There are two ways in which equilibria for this preference game can be defined. Also, when the preferences possess ever more features, we can gradually add more structures to the game. These include real-valued functions over return-distribution vectors, sets of probabilistic priors over states of the world, and eventually the traditional expected-utility framework involving one single prior. We establish equilibrium existence results, show the upper hemi-continuity of equilibrium sets over changing ambiguity attitudes, and uncover relations between the two versions of equilibria. Some attention is paid to the enterprising game, in which players exhibit ambiguity-seeking attitudes while betting optimistically on the favorable resolution of ambiguities. The two solution concepts are unified at this game’s pure equilibria, whose existence is guaranteed when strategic complementarities are present. The current framework can be applied to settings like auctions involving ambiguity on competitors’ assessments of item worths.

Higher Order Risk Attitudes and Prevention Under Different Timings of Loss

This paper provides experimental evidence of the role of higher order risk attitudes — especially prudence — in prevention behavior. Prudence, under an expected utility framework, increases (decreases) self-protection effort compared to the risk neutral level when the risk of losing part of an income exists in a future (the same) period. Motivated by these predictions that give the exact test on prudence, an experiment was designed where subjects go through higher order risk attitude elicitation and make a self-protection decision. In contrast to expected utility theory, the observed efforts are less than the risk neutral level, regardless of the timing of loss. This violation of expected utility predictions could be explained by probability weighting.

Game-Theoretic Modeling of Players’ Ambiguities on External Factors

We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on return-distribution vectors, essentially mappings from states of the world to distributions of returns to be received by players. There are two ways in which equilibria for this preference game can be defined. Also, when the preferences possess ever more features, we can gradually add more structures to the game. These include real-valued functions over return-distribution vectors, sets of probabilistic priors over states of the world, and eventually the traditional expected-utility framework involving one single prior. We establish equilibrium existence results, show the upper hemi-continuity of equilibrium sets over changing ambiguity attitudes, and uncover relations between the two versions of equilibria. Some attention is paid to the enterprising game, in which players exhibit ambiguity-seeking attitudes while betting optimistically on the favorable resolution of ambiguities. The two solution concepts are unified at this game's pure equilibria, whose existence is guaranteed when strategic complementarities are present. The current framework can be applied to settings like auctions involving ambiguity on competitors' assessments of item worths.