Ambiguity Aversion Research Articles

A Revealed Preference Test for Choquet and Max-Min Expected Utility with Ambiguity Aversion

We develop a revealed preference test for the Choquet expected utility model with ambiguity aversion, which does not rely on specific functional form assumptions on the utility index. It is computationally efficient if the number of states is not too large, even for a large number of observations. This is a nice feature compared to other existing revealed preference tests for decision models with ambiguity. We illustrate the usefulness of our results by implementing our test on two experimental datasets from the literature, and we compare the empirical fit of this model to the subjective expected utility model. (JEL C91, D81, D91, G41)

Consistent Depth of Reasoning in Level-k Models

Level-k models often assume that individuals employ a fixed depth of reasoning across different games. We study this assumption by having subjects make choices in five classes of games chosen to identify inconsistent depth of reasoning. We demonstrate that depth of reasoning is pervasively inconsistent, changing both within and between classes of games. We show that this cannot easily be explained by factors such as subject confusion, changing beliefs about others’ depth of reasoning, stochastic choice, model misspecification, changing incentives, or low cognitive ability. We develop a simple model incorporating ambiguity aversion that predicts inconsistent depth of reasoning. (JEL C57, C90, D81, D83, D91)

Data-Driven Shelf Stocking: Robustness and Vertical-Location Effect

In this article, we study a shelf-stock allocation problem in a data-driven setting where the demand distribution is unknown. The retailer needs to decide which commodities to place on each level of the shelf (location decision), and determine the stock level for each selected commodity at the shelf (stock decision) that can be adjusted based on updated demand prediction, under constraints on allocation and capacity, so as to maximize total expected profit. Key issues of the problem include demand endogeneity on vertical-location effect and the demand ambiguity that may arise from the ever shorter life cycles of commodities and other complicated determinants. We address the problem in a rolling-horizon fashion and develop a two-phase data-driven robust optimization model leveraging a decision-dependent Wasserstein metric that incorporates time-series demand forecasts and captures vertical-location effect under demand ambiguity. We derive tractable solution schemes for the model, in which the phase-I model determines the optimal location decision by solving one instance of mixed-integer linear program, while the phase-II model admits an analytical solution for updating the optimal stock. Furthermore, we discuss the sensitivity implications on how the ambiguity aversion impacts the optimal stock, and prove the consistency of the model solution under regularity condition on the underlying demand process that well justifies the asymptotic performance of the proposed data-driven approach. Finally, we extend our model to incorporate substitution effect, and conduct sufficient numerical experiments with real-life data that demonstrate the performance of our model.

Environmental management and restoration under unified risk and uncertainty using robustified dynamic Orlicz risk

Environmental management and restoration should be designed such that the risk and uncertainty owing to nonlinear stochastic systems can be successfully addressed. We apply the robustified dynamic Orlicz risk to the modeling and analysis of environmental management and restoration to consider both the risk and uncertainty within a unified theory. We focus on the control of a jump-driven hybrid stochastic system that represents macrophyte dynamics. The dynamic programming equation based on the Orlicz risk is first obtained heuristically, from which the associated Hamilton–Jacobi–Bellman (HJB) equation is derived. In the proposed Orlicz risk, the risk aversion of the decision-maker is represented by a power coefficient that resembles a certainty equivalence, whereas the uncertainty aversion is represented by the Kullback–Leibler divergence, in which the risk and uncertainty are handled consistently and separately. The HJB equation includes a new state-dependent discount factor that arises from the uncertainty aversion, which leads to a unique, nonlinear, and nonlocal term. The link between the proposed and classical stochastic control problems is discussed with a focus on control-dependent discount rates. We propose a finite difference method for computing the HJB equation. Finally, the proposed model is applied to an optimal harvesting problem for macrophytes in a brackish lake that contains both growing and drifting populations.

A robust financing theory of ICOs under demand uncertainty of products of token platforms

PurposeThe market products produced by Initial Coin Offerings (ICO) platforms are often relatively new and have no previous transaction records and therefore are hard to estimate for its demand. The purpose is to study the impacts of the degree of ambiguity aversion of entrepreneurs to demand uncertainty on the ICO financing ratio, the optimal expected output, the optimal efforts and the token price.Design/methodology/approachIn an optimal ICO design, we introduce demand uncertainty of the product and establish a robust optimization method to solve the ICO optimal design. We compare ICO financing and the general venture capital (VC) financing model. We analyze the impact of demand uncertainty on the optimal ICO financing ratio.FindingsFindings include that the ICO financing ratio is positively related to the degree of ambiguity aversion, the token price is negatively related to the degree of ambiguity aversion and the “ambiguity premium” exists in the ICO market, the optimal effort levels are negatively related with the ICO financing ratio, but positively related with token price, and in the environment of high production cost, VC financing is not as good as ICO financing.Originality/valueWe develop a robust ICO financing model by assuming that the entrepreneur is ambiguity aversive to the demand uncertainty. Analyze the impact of the degree of ambiguity aversion on the ICO financing ratio in theory and find that the entrepreneur can raise funds with the higher ICO token ratio when she has a larger degree of ambiguity aversion to the demand uncertainty. Extend the impact analysis of the degree of ambiguity aversion on the expected token price and find a negative relationship between the expected token price and the degree of ambiguity aversion of the entrepreneur to the demand uncertainty.

Ambiguity, information processing, and financial intermediation

This paper incorporates ambiguity and information processing constraints into the He and Krishnamurthy (2012) model of intermediary asset pricing. Financial intermediaries possess greater information processing capacity than households. In response, households optimally choose to delegate their investment decisions. The contractual relationship between households and intermediaries is subject to a moral hazard friction, which results in a financial constraint. We show that ambiguity aversion not only amplifies households' incentives to delegate but also tightens the financial constraint. The calibrated model can quantitatively explain both the unconditional and time-varying moments of observed asset prices while endogenously generating an empirically consistent crisis frequency.

Robust dynamic trading with realization utility

We incorporate model uncertainty into the intertemporal realized utility model proposed by Ingersoll and Jin (2013). We find: (1) model uncertainty erodes the investor’s value and makes him more willing to take the risk; (2) when ambiguity aversion is sufficiently high, voluntary realization of losses will not occur; (3) model uncertainty accelerates sales, thus shortening the average holding period and strengthening the disposition effect; (4) the disposition effect is weaker in the lower volatility case under model uncertainty, which is consistent with the empirical results; (5) model uncertainty alters the effect of volatility on the sale decision.

Exploring the psychological antecedents of suppliers' sustainability practices: A qualitative investigation in the Indian textile industry

AbstractThe uncertainties associated with modern businesses complicate decision‐making, especially in complex supply chains, such as those of the textile industry, which has its hub in emerging South Asian countries. Using the Indian textile industry as the research setting, this paper explores from a psychological lens how suppliers process uncertainties while adopting sustainability practices. The study uncovers certification agencies, interpersonal trust between suppliers and buyers, and suppliers' size, as key constructs that influence how suppliers perceive and process risks and ambiguities, and in turn how that influences their adoption of sustainability practices. Combining these empirical insights with the stakeholder and relational view theories, we develop a comprehensive framework to model suppliers' sustainability decision‐making in the face of uncertainty. This study uncovers nuances of uncertainty aversion, which provide valuable insights for practitioners while also breaking fertile ground for future academic research to quantify the emergent propositions.

Reinsurance contracts under Stackelberg game and market equilibrium

In this paper, we investigate the robust reinsurance contracts under Stackelberg game and market equilibrium. Each reinsurance contract contains two decision makers, one insurer and one reinsurer. The insurer is ambiguity-neutral and adopts a loss-dependent premium principle to collect premium. The reinsurer is ambiguity-averse and is a Bayesian learner. By using the stochastic dynamic programming method and the inverse method, the analytical expressions of the optimal risk allocation proportion and reinsurance price are derived for the two types of reinsurance contracts. We shows that the loss-dependent premium principle has the penalty-reward nature. Both the reinsurance price and demand decrease as the extrapolative intensity increases. Learning has important significance and always puts down the reinsurance price and puts up the reinsurance demand. On the contrary, the reinsurer’s ambiguity aversion raises the reinsurance price and decreases the reinsurance demand. Finally, numerical analysis reveals that the reinsurance price is greater under the Stackelberg game than that under the market equilibrium.

Robust Risk Control with Reinsurance and CAT Bonds

This research studies robust risk control policies for an ambiguity-averse insurer. The insurer can manage its risk exposure through the purchase of reinsurance and the issuance of parametric catastrophe (CAT) bonds, which are linked to an exogenous trigger index. The insurer worries about the veracity of the model and seeks to develop a robust strategy to minimize the discounted ruin probability. We allow the insurer to exhibit different levels of ambiguity aversion toward its own claims and the trigger index. By employing a robust control approach, we analytically derive the optimal risk control policies that provide the insurer with guidelines on how to effectively manage its risk in an ambiguous environment. We present numerical examples that showcase scenarios in which CAT bonds can be utilized as an effective risk mitigation tool. Furthermore, we assess the potential welfare losses that could arise if the insurer fails to account for model uncertainty or lacks the ability to issue CAT bonds.

Belief aggregation, updating and dynamic collective choice

This paper decision-theoretically investigates the belief aggregation method which allows consistently updating the aggregate belief.After confirming that the Pareto axiom and dynamic consistency require the decision power of an individual to evolve proportionally to how much his/her prior has been successful, we propose a weaker Pareto axiom that applies only to one-step-ahead uncertainties and puts no restriction on how the decision powers should evolve.We show in the binary tree domain that taking the median belief satisfies the proposed axiom, even full ex-ante efficiency under a single-crossing condition and that dynamic voting implements it.Finally, we investigate the role of ambiguity aversion.

Endogenous Aggregate Beliefs: Equity Trading under Heterogeneity in Ambiguity Aversion

We build a simple and tractable model of consumer heterogeneity in ambiguity aversion and use it to illustrate how asymmetric beliefs in the asset markets affect the dynamics of asset pricing, portfolio allocation, and the wealth distribution. The model is an otherwise canonical exchange-economy setting with two aggregate states of nature and two assets. The key focus is on how asset prices, when subjected to ambiguity, behave very differently in the short run than in the long run. In the short run, heterogeneity plays an important role. In the long run, belief heterogeneity persists, but the wealth distribution has evolved so that only the least ambiguity-averse investors matter for prices. As part of the short-run dynamics, the model can generate endogenous aggregate movements in non-participation—a drastic form of trading less—in response to ambiguity, with strong depressing effects on asset prices.

Discrete Choquet integral aggregation applied to intertemporal choices: financial literacy components and gender in anomalies and uncertainty aversion

Discrete Choquet integral aggregation applied to intertemporal choices: financial literacy components and gender in anomalies and uncertainty aversion

Ambiguity, limited market participation, and the cross-sectional stock return

Using expected utility under uncertain probability theory (EUUP, Izhakian, 2017, 2020), we study whether the ambiguity related to individual stocks is priced in the Chinese A-share market and the mechanism behind the ambiguity premium phenomenon. Theoretically, when the asset price is within a specific range, ambiguity-averse investors refrain from participating in trading. As asset ambiguity increases, high ambiguity-averse investors exit the market, with those with lower aversion remaining in the market (limited market participation phenomenon). Investors who remain in the market due to lower ambiguity aversion are willing to accept a low ambiguity premium. Empirically, we measure monthly ambiguity using the volatility of daily stock return distributions within a month and find the following: (1) The equal-weighted average returns of the most ambiguous portfolios (top 20%) are significantly lower than those of the least ambiguous portfolios (bottom 20%). (2) Ambiguity still significantly negatively affects the cross-sectional stock return after controlling for common firm characteristics. (3) The higher the ambiguity, the lower the future trading activity, supporting our theoretical predictions. These findings reveal the mechanism of the negative ambiguity premium in the Chinese A-share market. This study provides new ideas for building a factor-pricing model suitable for the A-share market and a fresh perspective for preventing systemic financial risk.

Randomization advice and ambiguity aversion

We design and implement lab experiments to evaluate the normative appeal of behavior arising from models of ambiguity-averse preferences. We report two main empirical findings. First, we demonstrate that behavior reflects an incomplete understanding of the problem, providing evidence that subjects do not act on the basis of preferences alone. Second, additional clarification of the decision making environment pushes subjects’ choices in the direction of ambiguity aversion models, regardless of whether or not the choices are also consistent with subjective expected utility, supporting the position that subjects find such behavior normatively appealing.

Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity

This paper studies the optimal consumption, investment, health insurance and life insurance strategy for a wage earner with smooth ambiguity, habit formation and biometric risks. The individual can invest in the financial market composed of a risk-free asset and a risky asset whose unknown market price results in ambiguity. The habit formation depends on historical consumption and satisfies an ordinary differential equation. Moreover, the biometric risks, which consist of health shock risk and mortality risk, can impact the individual's income and health state. The individual can purchase health insurance and life insurance to respectively deal with health shock risk and mortality risk, and aims at maximizing the total expected utility of consumption, legacy and terminal wealth. Using the dynamic programming technique, we derive the corresponding Hamilton-Jacobi-Bellman equation in the states of health and critical illness respectively, prove the verification theorem and obtain closed-form solutions for the optimal strategies. Finally, numerical experiments are carried out to illustrate the impact of risk aversion, ambiguity aversion, health shock and habit formation on the optimal strategy. The results reveal that the wage earner with different utility functions and different health states will show different behaviors in consumption, investment and insurance purchase.

How Numerical Cognition Explains Ambiguity Aversion

Abstract Consumers generally prefer precise probabilities or outcomes over imprecise ranges with the same expected value, a bias known as “ambiguity aversion.” We argue that two elementary principles of numerical cognition explain great heterogeneity in this bias, affecting consumer choices in many domains where options are characterized by varying levels of uncertainty (e.g., lotteries, discounts, investment products, vaccines, etc.). The first principle, the “compression effect,” stipulates that consumers’ mental number lines are increasingly compressed at greater number magnitudes. This alone suffices to predict ambiguity aversion as it causes a midpoint (e.g., $40) to be perceived as closer to the upper bound of a range (e.g., $60) compared to its lower bound (e.g., $20). Furthermore, as the compression effect distorts the mental number line especially at lower numbers, it follows that ambiguity aversion should decrease around greater numbers. The second principle, the “left-digit effect” causes a range’s relative attractiveness to decrease (increase) disproportionately with every left-digit transition in its lower (upper) bound, thus increasing (decreasing) ambiguity aversion. Due to the overall compression effect, the impact of the left-digit effect increases at greater numbers. We present 34 experiments (N = 10,634) to support the theory’s predictions and wide applicability.

Pricing airbag option via first passage time approach

Airbag option is a new structured product that has been highly favored by investors in the over-the-counter derivatives market. It provides protections against the downside loss to investors like the ‘airbag’ in a car crash. In contrast with its popularity, there is little literature on the pricing of airbag options, especially from the mathematical finance point of view. In this paper, we study the pricing of airbag options using the first passage time approach. We propose two innovative new types of airbag options, namely airbag-TB and airbag-ER, which enhance the downside loss protections by integrating a time-varying barrier and early redemption features respectively in the payoffs. Explicit and closed-form pricing formulas for the original and the two new types of airbag options are derived under the mixed-exponential jump diffusion (MEJD) model, double exponential jump diffusion (DEJD) model and Black-Scholes (BS) model. In doing so, we significantly improve the Hybrid model proposed by Jaimungal and Sigloch (Incorporating risk and ambiguity aversion into a hybrid model of default. Math. Finance, 2012, 22, 57–81) by incorporating a stochastic redemption intensity model and more general underlying asset dynamics. We further demonstrate the performance of our pricing formulas and the two new types of airbag options with numerical examples based on Monte Carlo simulation, which verifies the accuracy and efficiency of our pricing formulas.

Uncertainty premia for small and large risks

We develop a model showing that the effect of smooth ambiguity aversion on large risks, those that are independent of the holding period, is of first-order importance, in contrast to risks that are proportional to the holding period. To test this hypothesis, we construct an ex-ante measure of the price of uncertainty based on changes in the option-implied concavity of preferences. As predicted by our model, we find that such concavity increases ahead of scheduled macroeconomic announcements, which represent large risks. We also provide an estimate of the coefficient of relative ambiguity aversion and show how uncertainty varies across different announcements. Our results suggest that the macroeconomic announcement premium arises at least partly because of an increase in the price of uncertainty. One implication is that a fundamental benefit of securities markets is that they break large risks into small ones by allowing frequent trading, thereby reducing discount rates.

Between evidence and delusion – a scoping review of cognitive biases in Environmental and Sustainability Education

Exposing learners to sustainability-related topics can present affective–motivational challenges for learners, which may prompt cognitive bias. Cognitive bias directly influences how individuals perceive and process sustainability-related information, thereby also influencing sustainability-related behaviour and decision-making. Therefore, cognitive bias may also present a significant obstacle to the purposes of Environmental and Sustainability Education. Notwithstanding its potential relevance, there is no comprehensive understanding of how cognitive bias is currently addressed in Environmental and Sustainability Education. This review scopes scientific literature that addresses cognitive bias in Environmental and Sustainability education, based on SCOPUS, Web of Science and ERIC. We identified 21 articles that matched our search criteria. We identified four superordinate categories of cognitive bias that were addressed in the literature, including bounded rationality, confirmation bias, self-enhancement and ambiguity aversion. Moreover, we distinguished three perspectives from which cognitive bias is discussed in the literature: (i) education to mitigate bias associated with sustainability-related matters, (ii) bias as a barrier to Environmental and Sustainability Education and (iii) bias at the research-paradigm level. The list of identified biases provides evidence that cognitive bias may play an important role in Environmental and Sustainability Education scholarship and practices, which suggests that more research on this topic is needed.