Ambiguity Averse Decision Maker Research Articles

Prolonged Learning and Hasty Stopping: The Wald Problem with Ambiguity

This paper studies sequential information acquisition by an ambiguity-averse decision-maker (DM), who decides how long to collect information before taking an irreversible action. The agent optimizes against the worst-case belief and updates prior by prior. We show that the consideration of ambiguity gives rise to rich dynamics: compared to the Bayesian DM, the DM here tends to experiment excessively when facing modest uncertainty and, to counteract it, may stop experimenting prematurely when facing high uncertainty. In the latter case, the DM’s stopping rule is nonmonotonic in beliefs and features randomized stopping. (JEL C61, D81, D83, D91)

OPTIMAL INSURANCE CONTRACTS UNDER DISTORTION RISK MEASURES WITH AMBIGUITY AVERSION

AbstractThis paper presents analytical representations for an optimal insurance contract under distortion risk measure and in the presence of model uncertainty. We incorporate ambiguity aversion and distortion risk measure through the model of Robert and Therond [(2014) ASTIN Bulletin: The Journal of the IAA, 44(2), 277–302.] as per the framework of Klibanoff et al. [(2005) A smooth model of decision making under ambiguity. Econometrica, 73(6), 1849–1892.]. Explicit optimal insurance indemnity functions are derived when the decision maker (DM) applies Value-at-Risk as risk measure and is ambiguous about the loss distribution. Our results show that: (1) under model uncertainty, ambiguity aversion results in a distorted probability distribution over the set of possible models with a bias in favor of the model which yields a larger risk; (2) a more ambiguity-averse DM would demand more insurance coverage; (3) for a given budget, uncertainties about the loss distribution result in higher risk level for the DM.

Limit Orders under Knightian Uncertainty

Ambiguity averse decision-makers can behave in financial portfolio problems in ways that cannot be rationalized as subjective expected utility maximization. Indeed, [Dow and da Costa Werlang, Econometrica 1992] show that an ambiguity-averse decision-maker might abstain from trading an asset for a wide interval of prices; something no subjective expected utility maximizer can. Dow and da Costa Werlang assume that decision-makers know the price of an asset when trading. We show that when markets operate via limit orders instead, all investment behavior of an ambiguity-averse decision-maker is observationally equivalent to the behavior of a subjective expected utility maximizer with the same risk preferences; ambiguity aversion has no additional explanatory power.

A Theory of Experimenters: Robustness, Randomization, and Balance

This paper studies the problem of experiment design by an ambiguity-averse decision-maker who trades off subjective expected performance against robust performance guarantees. This framework accounts for real-world experimenters’ preference for randomization. It also clarifies the circumstances in which randomization is optimal: when the available sample size is large and robustness is an important concern. We apply our model to shed light on the practice of rerandomization, used to improve balance across treatment and control groups. We show that rerandomization creates a trade-off between subjective performance and robust performance guarantees. However, robust performance guarantees diminish very slowly with the number of rerandomizations. This suggests that moderate levels of rerandomization usefully expand the set of acceptable compromises between subjective performance and robustness. Targeting a fixed quantile of balance is safer than targeting an absolute balance objective. (JEL C90, D81)

Optimizing surveillance strategies for early detection of invasive alien species

Surveillance programs to detect alien invasive pests seek to find them as soon as possible, but also to minimize the cost of damage from invasion. To examine the trade-offs between these objectives, we developed an economic model that allocates survey sites to minimize either the expected mitigation costs or the expected time until first detection of an invasive alien pest subject to a budget constraint on surveillance costs. We also examined strategies preferred by ambiguity-averse decision makers that minimize the expected and worst-case outcomes of each performance measure. We applied the model to the problem of detecting Asian longhorned beetle (Anoplophora glabripennis) in the Greater Toronto Area, Canada, one of the most harmful invasive alien insects in North America. When minimizing expected mitigation costs or expected time to detection, the trade-off between these survey objectives was small. Strategies that minimize the worst-case mitigation costs differed sharply and surveyed sites with high host densities using high sampling intensities whereas strategies that minimize the worst detection times surveyed sites across the entire area using low sampling intensities. Our results suggest that preferences for minimizing mitigation costs or time to detection are more consequential for ambiguity-averse managers than they are for risk-neutral decision-makers.

Ordering ambiguous acts

We investigate what it means for one act to be more ambiguous than another. The question is evidently analogous to asking what makes one prospect riskier than another, but beliefs are neither objective nor representable by a unique probability. Our starting point is an abstract class of preferences constructed to be (strictly) partially ordered by a more ambiguity averse relation. First, we define two notions of more ambiguous with respect to such a class. A more ambiguous (I) act makes an ambiguity averse decision maker (DM) worse off but does not affect the welfare of an ambiguity neutral DM. A more ambiguous (II) act adversely affects a more ambiguity averse DM more, as measured by the compensation they require to switch acts. Unlike more ambiguous (I), more ambiguous (II) does not require indifference of ambiguity neutral elements to the acts being compared. Second, we implement the abstract definitions to characterize more ambiguous (I) and (II) for two explicit preference families: α-maxmin expected utility and smooth ambiguity. Thirdly, we give applications to the comparative statics of more ambiguous in a standard portfolio problem and a consumption-saving problem.

Comparisons of Ambiguous Experiments

An ambiguous statistical experiment is a set of joint probability distributions over states and signals. This note compares ambiguous experiments from the point of view of an ambiguity averse decision maker and extends the Blackwell (1951, 1953) ordering to this setting.

Ambiguous Jump-Diffusions and Optimal Stopping

An ambiguity averse decision-maker contemplates investment of a fixed size capital into a project with a stochastic profit stream under the Knightian uncertainty. Multiple priors are modeled as a "cloud" of diffusion processes with embedded compound Poisson jumps. The "cloud" contains the Brownian motion (BM) as a process with zero density of jumps. The decision-maker has recursive multiple priors utility as in Epstein and Schneider (2003) and chooses the optimal investment timing. We demonstrate that if the expected present value (EPV) of the project is the same for each jump-diffusion prior at the moment of investment, then the BM is the worst prior in the waiting region. The same conclusion holds for some parameter values even when the BM gives the highest EPV of the project. For other parameter values, it is possible that the local dynamics of the worst case prior is given by a jump-diffusion in a vicinity of the investment threshold and by the BM in a vicinity of negative infinity. Explicit formulas for the value functions and investment thresholds are derived.

Optimal decision under ambiguity for diffusion processes

In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brownian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in a two-parameter function space. In a second part we solve optimal stopping problems when the underlying process may crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. Examples are discussed.

The best choice problem under ambiguity

We model and solve best choice problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. The agent faces ambiguity about the probability that a candidate—a relatively top applicant—is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using backward induction. As in the classical case, the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule.

Optimal Stopping Under Ambiguity

We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super)martingales, provide a Doob-Meyer decomposition, and characterize minimax martingales. This allows us to extend the standard backward induction procedure to ambiguous, time-consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree. We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).

Ambiguity aversion and the absence of indexed debt

Following the seminal works of Schmeidler (1989), Gilboa and Schmeidler (1989), roughly put, an agent’s subjective beliefs are said to be ambiguous if the beliefs may not be represented by a unique probability distribution, in the standard Bayesian fashion, but instead by a set of probabilities. An ambiguity averse decision maker evaluates an act by the minimum expected value that may be associated with it.

A survey of some applications of the idea of ambiguity aversion in economics

Subjective uncertainty is characterized by ambiguity if the decision maker has an imprecise knowledge of the probabilities of payoff relevant events. In such an instance, the decision maker's beliefs are better represented by a set of probability functions than by a unique probability function. An ambiguity averse decision maker adjusts his choice on the side of caution in response to his imprecise knowledge of the odds. This paper attempts a (selective) survey of some of the achievements of the research program which has analyzed important economic phenomena using a methodology that departs from standard paradigm by explicitly allowing for ambiguity aversion. We specifically look at applications, and implications, of ambiguity aversion in three areas: design of bilateral economic contracts, the trade in financial contracts and financial markets and finally, strategic decision making in auctions. We also indicate the possible relevance of these findings to recent research in AI.