Heuristic arguments for probabilistic sensitivity and rank dependence

Measurements of volatile and residue burning times of captive coal particles have shown them to vary in proportion to the square of the initial particle diameter; this was true for each of 10 coals tested. For the volatiles, the measured constant of proportionality was found to be independent of coal rank when allowance was made for swelling, the burning rate apparently being controlled by the diffusional rate of volatile escape through a porous matrix of fixed carbon. For the residues, the experimental “square-law” relation confirms Nusselt’s prediction; and agreement between predicted and experimental values of the proportionality constant was found to be good. An apparent rank dependence, showing shorter burning times with less fixed carbon, was simply a consequence of there being less fixed carbon to burn. There was no influence of rank-dependent “reactivity.” The relevance of the results to flames is also discussed.

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97/00767 Coal solubilization accelerated by reductive methylation under ultrasonic irradiation and its coal rank dependence

Fuel and Energy Abstracts ◽

10.1016/s0140-6701(97)82573-8 ◽

1997 ◽

Vol 38 (2) ◽

pp. 69

Keyword(s):

Ultrasonic Irradiation ◽

Coal Rank ◽

Reductive Methylation ◽

Coal Solubilization ◽

Rank Dependence

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Applications and extensions of rank dependence

Prospect Theory ◽

10.1017/cbo9780511779329.010 ◽

2012 ◽

pp. 203-233

Author(s):

Peter P. Wakker

Keyword(s):

Rank Dependence

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Risk Exchange with Distorted Probabilities

Astin Bulletin ◽

10.1017/s051503610001446x ◽

2006 ◽

Vol 36 (1) ◽

pp. 219-243 ◽

Cited By ~ 21

Author(s):

Andreas Tsanakas ◽

Nicos Christofides

Keyword(s):

Decision Making ◽

Real World ◽

Heterogeneous Agents ◽

Ambiguity Aversion ◽

Asset Returns ◽

Market Risk ◽

Exchange Economy ◽

Important Distinction ◽

Distortion Functions ◽

Rank Dependence

An exchange economy is considered, where agents (insurers/banks) trade risks. Decision making takes place under distorted probabilities, which are used to represent either rank-dependence of preferences or ambiguity with respect to real-world probabilities. Pricing formulas and risk allocations, generalising the results of Bühlmann (1980, 1984) are obtained via the construction of aggregate preferences from heterogeneous agents’ utility and distortion functions. This involves the introduction of a novel ‘collective ambiguity aversion’ coefficient. It is shown that probability distortion changes insurers’ behaviour, who trade not only to share the aggregate market risk, but are also found to bet against each other. Moreover, probability distortion tends to increase the price of insurance (increase asset returns). While the cases of rank-dependence and ambiguity are formally similar, an important distinction emerges as for rank-dependent preferences equilibria are determinate, while for ambiguity they are generally indeterminate.

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Risk, Ambiguity, and the Rank-Dependence Axioms

The American Economic Review ◽

10.1257/aer.99.1.385 ◽

2009 ◽

Vol 99 (1) ◽

pp. 385-392 ◽

Cited By ~ 102

Author(s):

Mark J Machina

Keyword(s):

Expected Utility ◽

Subjective Expected Utility ◽

Choquet Expected Utility ◽

Risk Ambiguity ◽

Rank Dependence ◽

Nonseparable Models ◽

Utility Preferences

Choice problems in the spirit of Ellsberg (1961) suggest that rank-dependent (“Choquet expected utility”) preferences over subjective gambles might be subject to the same difficulties that Ellsberg's earlier examples posed for subjective expected utility. These difficulties stem from event-separability properties that rank-dependent preferences partially retain from expected utility, and suggest that nonseparable models of preferences might be better at capturing features of behavior that lead to these paradoxes. (JEL D81)

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