Loss-Aversion with Kinked Linear Utility Functions

Best, Michael J.; Grauer, Robert R.; Hlouskova, Jaroslava; Zhang, Xili

doi:10.1007/s10614-013-9391-x

Cited by 10 publications

(3 citation statements)

References 23 publications

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“…One of the most influential theories in decision theory is prospect theory (Kahneman & Tversky, 1979;Tversky & Kahneman, 1992), which posits distortions of objective probabilities. Optimization processes using this theory are quite complex and often require algorithmic solutions (e.g., Best et al, 2014;De Giorgi et al, 2007;Gong et al, 2018). A direction for future research would be to study the relevance of insensitivity regions in financial applications, such as those in the aforementioned papers.…”

Section: Summary and Concluding Notesmentioning

confidence: 99%

The Slicing Method: Determining Insensitivity Regions of Probability Weighting Functions

2022

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A popular rule of thumb, usually called ''heuristic technique'' in Behavioral Economics, for determining the likelihood insensitivity regions of probability weighting functions (pwf's) is based on searching for points at which the pwf's are twice their values at half the points. Although this technique works remarkably well for many commonly used pwf's, it sometimes fails to provide the correct answer. In order to cover the class of pwf's for which the heuristic technique does not work, in this paper we propose, discuss, and illustrate an extension of the technique into what we call the ''slicing method,'' which is capable of finding the subadditivity and insensitivity regions of any continuous pwf.

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Section: Summary and Concluding Notesmentioning

confidence: 99%

The Slicing Method: Determining Insensitivity Regions of Probability Weighting Functions

2022

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“…The utility is a monotonic, concave transformation of the pay-off. Common examples of utility functions are exponential utility [4] and the piecewise linear utility [2]. Since our problem is formulated in terms of cost rather than pay-off, we model risk aversion as minimization of the expected disutility.…”

Section: Problem Descriptionmentioning

confidence: 99%

Now, Later, or Both: A Closed-Form Optimal Decision for a Risk-Averse Buyer

Hoogland

Weerdt

Poutré

2017

Lecture Notes in Business Information Processing

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Motivated by the energy domain, we examine a risk-averse buyer that has to purchase a fixed quantity of a continuous good. The buyer has two opportunities to buy: now or later. The buyer can spread the quantity over the two timeslots in any way, as long as the total quantity remains the same. The current price is known, but the future price is not. It is well known that risk neutral buyers purchase in whichever timeslot they expect to be the cheapest, regardless of the uncertainty of the future price. Research suggests, however, that most people may in fact be risk-averse. If the expected future price is lower than the current price, but very uncertain, then they may purchase in the present, or spread the quantity over both timeslots. We describe a formal model with a uniform price distribution and a two-segment piecewise linear risk aversion function. We provide a theorem that states the optimal decision as a closed-form expression.

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“…Constraints (3) and (4) are the budget and margin constraints, respectively. We solve the system given by the objective function (1) subject to the constraints (2)-(4) using the algorithm described in Best et al (2014) and Best and Zhang (2011). In order to overcome the problem of non-differentiability at the kink point Best, Grauer, Hlouskova and Zhang transformed the kinked linear utility problem into a higher dimensional linear program which is differentiable.…”

Section: The Modelmentioning

confidence: 99%