Loss aversion with a state-dependent reference point

This study investigates loss aversion when the reference point is a state-dependent random variable. This case describes, for example, a money manager being evaluated relative to a risky benchmark index rather than a fixed target return level. Using a state-dependent structure, prospects are more (less) attractive if they depend positively (negatively) on the reference point. In addition, the structure avoids an inherent aversion to risky prospects and yields no losses when the prospect and the reference point are the same. Related to this, the optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) when the reference point is selected completely endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. For example, the typical investment benchmark index is externally fixed by the investment principal for the duration of the investment mandate. We develop a choice model where adjustment costs cause stickiness relative to an initial exogenous reference point.Reference-dependent preferences, stochastic reference point, loss aversion, disappointment theory, regret theory.

Loss Aversion with a State-dependent Reference Point

This study investigates loss aversion when the reference point is state-dependent. Using a state-dependent structure, prospects are more attractive if they depend positively on the reference point and are less attractive in case of negative dependence. In addition, the structure is neutral in the sense that it avoids an inherent aversion to risky prospects and yields no loss when the prospect and the reference point are the same. Related to this, the preferred personal equilibrium equals the optimal consumption solution when the reference point is selected completely endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component

Loss Aversion with a State-Dependent Reference Point

This study investigates reference-dependent choice with a stochastic, state-dependent reference point. The optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) if the reference point is selected fully endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. We develop a choice model in which adjustment costs can cause stickiness relative to an initial, exogenous reference point. Using historical U.S. investment benchmark data, we show that this model is consistent with diversification across bonds and stocks for a wide range of evaluation horizons, despite the historically high-risk premium of stocks compared to bonds

Reference-Dependent Stochastic User Equilibrium with Endogenous Reference Points

We consider the application of reference-dependent consumer choice theory to traffic assignment on transportation networks. Route choice is modelled based on random utility maximisation with systematic utility embodying loss aversion for the travel time and money expenditure attributes. Stochastic user equilibrium models found in the literature have considered exogenously given reference points. The paper proposes a model where reference points are determined consistently with the equilibrium flows and travel times. The referencedependent stochastic user equilibrium (RDSUE) is defined as the condition where (i) no user can improve her utility by unilaterally changing path, (ii) each user has as reference point the current travel time and the money expenditure of one of the available paths, and (iii) if each user updates the reference point to her current path the observed path flows do not change. These conditions are formally equivalent to a multi-class stochastic equilibrium where each class is associated with a path and has as reference point the current state on the path, and the number of users in each class equals the current flow on the path. The RDSUE is formulated as a fixed point problem in the path flows. Existence of RDSUE is guaranteed under usual assumptions. A heuristic algorithm based on the method of successive averages is proposed to solve the problem. The model is illustrated by two numerical examples, one relates to a two-link network and another to the Nguyen-Dupuit network. A reference-dependent route choice model calibrated on stated preference data is used. The second example serves also to demonstrate the algorithm. The impact on the equilibrium of different assumptions on the degree of loss aversion with respect to the travel time attribute are investigated

Primate anterior insular cortex represents economic decision variables postulated by Prospect theory

Humans and animals need to make decisions under various degrees of uncertainty. These decisions are strongly influenced by an individual's risk attitude. Substantial studies have demonstrated that one’s risk attitude can vary substantially across different behavioral contexts. For instance, humans and animals show different risk attitudes when facing risky gains versus risky losses. The abundance of resources in the environment and the current wealth of subjects also modulate an individual's risk attitude. Prospect theory, the most successful and wide-ranging descriptive model of decision-making under risk, explains these behavioral effects using the concepts of a reference point and loss aversion. However, at present, prospect theory cannot be clearly interpreted in terms of neuronal mechanisms. None of the known structures or processes involved in decision-making in the primate brain has been convincingly related to the two key concepts: reference point dependence and loss aversion. Based on human imaging and lesion studies, we hypothesized that the anterior insular cortex (AIC) may be the candidate that represents the current state of the subject (the reference point) as well as reference-dependent value signals that differ in loss or gain context (asymmetrical value functions in loss and gain) suggested by prospect theory. Using a new token gambling task, we found that macaques, like humans, change their risk attitude across wealth levels and gain/loss contexts. In addition, monkeys’ risk behaviors were well explained with a wealth-dependent prospect theory model. Furthermore, neurons in the primate AIC monitor contextual factor that influence monkey’s risk attitudes. Many AIC neurons encoding the wealth level of the monkey as well as the expected value of options in a gain/loss specific manner. A subset of AIC neurons can further predict inter-trial fluctuations of the monkey’s risk attitude. These findings suggest a role of the primate AIC in representing economic gain and loss relative to a reference point and in influencing the likelihood of accepting a risk during uncertain decisions. We anticipate our finding to be a starting point for thoughtful investigation of neural implementation of core components in the prospect theory

Reference Points and Effort Provision

A key open question for theories of reference-dependent preferences is what determines the reference point. One candidate is expectations: what people expect could affect how they feel about what actually occurs. In a real-effort experiment, we manipulate the rational expectations of subjects and check whether this manipulation influences their effort provision. We find that effort provision is significantly different between treatments in the way predicted by models of expectation-based reference-dependent preferences: if expectations are high, subjects work longer and earn more money than if expectations are low

Monopoly pricing when consumers are antagonized by unexpected price increases: a "cover version" of the Heidhues-Koszegi-Rabin model

This paper reformulates and simpli�fies a recent model by Heidhues and Koszegi (2005), which in turn is based on a behavioral model due to Koszegi and Rabin (2006). The model analyzes optimal pricing when consumers are loss averse in the sense that an unexpected price hike lowers their willingness to pay. The main message of the Heidhues-Koszegi model, namely that this form of consumer loss aversion leads to rigid price responses to cost fluctuations, carries over. I demonstrate the usefulness of this "cover version" of the Heidhues-Koszegi-Rabin model by obtaining new results: (1) loss aversion lowers expected prices; (2) the firm's incentive to adopt a rigid pricing strategy is stronger when fluctuations are in demand rather than in costs

Uncertain Demand, Consumer Loss Aversion, and Flat-Rate Tariffs

The so called flat-rate bias is a well documented phenomenon caused by consumers' desire to be insured against fluctuations in their billing amounts. This paper shows that expectation-based loss aversion provides a formal explanation for this bias. We solve for the optimal two-part tariff when contracting with loss-averse consumers who are uncertain about their demand. The optimal tariff is a flat rate if marginal cost of production is low compared to a consumer's degree of loss aversion and if there is enough variation in the consumer's demand. Moreover, if consumers differ with respect to the degree of loss aversion, firms' optimal menu of tariffs typically comprises a flat-rate contract

The Expectation-Based Loss-Averse Newsvendor

We modify the classic single-period inventory management problem by assuming that the newsvendor is expectation-based loss averse according to Koszegi and Rabin (2006, 2007). Expectation-based loss aversion leads to an endogenous psychological cost of leftovers as well as stockouts. If there are no monetary stockout costs, then the loss-averse newsvendor orders a quantity lower than the quantity ordered by a profit-maximizing newsvendor. If there are positive monetary costs associated with stockouts, then the loss-averse newsvendor places suboptimal orders, which can be either too high or too low

Optimistic versus Pessimistic--Optimal Judgemental Bias with Reference Point

This paper develops a model of reference-dependent assessment of subjective beliefs in which loss-averse people optimally choose the expectation as the reference point to balance the current felicity from the optimistic anticipation and the future disappointment from the realisation. The choice of over-optimism or over-pessimism depends on the real chance of success and optimistic decision makers prefer receiving early information. In the portfolio choice problem, pessimistic investors tend to trade conservatively, however, they might trade aggressively if they are sophisticated enough to recognise the biases since low expectation can reduce their fear of loss