scholarly journals Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures

2021 ◽  
Author(s):  
Godfrey Cadogan
Keyword(s):  
Probability Measures ◽  
Value Functions ◽  
Stochastic Choice ◽  
Class Theory ◽  
Binary Operations ◽  
Choice Sets ◽  
Empirical Probability ◽  
Designed Experiment ◽  
Set Up ◽  
Gain Loss

We introduce a monotone class theory of Prospect Theory's value functions, which shows that they can be replaced almost surely by a topological lifting comprised of a class of compact isomorphic maps that embed weakly co-monotonic probability measures, attached to state space, in outcome space. Thus, agents solve a signal extraction problem to obtain estimates of empirical probability weights for prospects under risk and uncertainty. By virtue of the topological lifting, we prove an almost sure isomorphism theorem between compact stochastic choice operators, and well defined outcomes which, under Brouwer-Schauder theory, guarantees fixed point convergence in convex choice sets. Along the way we introduce a risk operator in the Hoffman-Jorgensen class of lifting operators, and value function [averaging] operators with respect to Radon measure. In that set up, suitable binary operations on gain-loss space show that our risk operator is isometric for gains and skewed for losses. The point spectrum from this operator constitutes the range of admissible observations for loss aversion index in a well designed experiment.

scholarly journals Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures

2021 ◽  
Author(s):  
Godfrey Cadogan
Keyword(s):  
Probability Measures ◽  
Value Functions ◽  
Stochastic Choice ◽  
Class Theory ◽  
Binary Operations ◽  
Choice Sets ◽  
Empirical Probability ◽  
Designed Experiment ◽  
Set Up ◽  
Gain Loss

We introduce a monotone class theory of Prospect Theory's value functions, which shows that they can be replaced almost surely by a topological lifting comprised of a class of compact isomorphic maps that embed weakly co-monotonic probability measures, attached to state space, in outcome space. Thus, agents solve a signal extraction problem to obtain estimates of empirical probability weights for prospects under risk and uncertainty. By virtue of the topological lifting, we prove an almost sure isomorphism theorem between compact stochastic choice operators, and well defined outcomes which, under Brouwer-Schauder theory, guarantees fixed point convergence in convex choice sets. Along the way we introduce a risk operator in the Hoffman-Jorgensen class of lifting operators, and value function [averaging] operators with respect to Radon measure. In that set up, suitable binary operations on gain-loss space show that our risk operator is isometric for gains and skewed for losses. The point spectrum from this operator constitutes the range of admissible observations for loss aversion index in a well designed experiment.

Sustainability Evaluation of Low Carbon Technology and Transition Plan of Building Industry in Chongming, Shanghai

2011 ◽  
Vol 347-353 ◽  
pp. 2933-2937
Author(s):  
Bei Jia Huang ◽  
Hai Zhen Yang ◽  
Guo Ru ◽  
Shao Ping Wang
Keyword(s):  
Ghg Emissions ◽  
Assessment Method ◽  
Assessment System ◽  
Building Industry ◽  
Value Functions ◽  
Low Carbon ◽  
Co2 Emission Reduction ◽  
Industry Development ◽  
Ghg Reduction ◽  
Set Up

In order to meet the GHG reduction and sustainable goals in industry development, we need those strategies that are not only reducing GHG emissions but also not compromising other economic, environmental and social priorities. The low carbon and sustainable requirements in industry development are analyzed by reviewing the existing related researches. Multi-Attributive Assessment method is selected as the most appropriate one for the study. Indicators and utility value functions of the assessment system are accordingly set up. Building industry in Chongming, Shanghai is analyzed as case study. Most potential technologies and their preferential order are figured out after evaluation. CO2 emission reduction requirement in 2015 is worked out as 0.68 t for low carbon scenario and 1.36t for ideal scenario. Required building area is then calculated. Results show the low carbon scenario is possible to meet if the existing and new construction buildings can well apply the selected technologies.

scholarly journals Large Deviation Theorems for Empirical Probability Measures

1979 ◽  
Vol 7 (4) ◽  
pp. 553-586 ◽  
Author(s):  
P. Groeneboom ◽  
J. Oosterhoff ◽  
F. H. Ruymgaart
Keyword(s):  
Large Deviation ◽  
Probability Measures ◽  
Empirical Probability

scholarly journals DYNAMIC CONIC FINANCE: PRICING AND HEDGING IN MARKET MODELS WITH TRANSACTION COSTS VIA DYNAMIC COHERENT ACCEPTABILITY INDICES

2013 ◽  
Vol 16 (01) ◽  
pp. 1350002 ◽  
Author(s):  
TOMASZ R. BIELECKI ◽  
IGOR CIALENCO ◽  
ISMAIL IYIGUNLER ◽  
RODRIGO RODRIGUEZ
Keyword(s):  
Transaction Costs ◽  
Risk Measures ◽  
Probability Measures ◽  
Coherent Risk ◽  
Conic Finance ◽  
Bid Prices ◽  
Path Dependent ◽  
Gain Loss ◽  
Risk Neutral Measures ◽  
Dynamic Gain

In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of Asset Pricing using the dynamic coherent risk measures. We introduce the dynamic ask and bid prices of a derivative contract in markets with transaction costs. Based on these results, we derive a representation theorem for the dynamic bid and ask prices in terms of dynamically consistent sequence of sets of probability measures and risk-neutral measures. To illustrate our results, we compute the ask and bid prices of some path-dependent options using the dynamic Gain-Loss Ratio.

scholarly journals You cannot accurately estimate an individual’s loss aversion using an accept-reject task

2020 ◽  
Author(s):  
Lukasz Walasek ◽  
Neil Stewart
Keyword(s):  
Prospect Theory ◽  
Loss Aversion ◽  
Model Parameters ◽  
Probability Weighting ◽  
Value Functions ◽  
Trade Off ◽  
Simple Version ◽  
The Poor ◽  
Gain Loss ◽  
Linear Probability

Prospect theory's loss aversion is often measured in the accept-reject task, in which participants accept or reject the chance of playing a series of gambles. The gambles are two-branch 50/50 gambles with varying gain and loss amounts (e.g., 50% chance of winning $20 and a 50% chance of losing $10). Prospect theory quantifies loss aversion by scaling losses up by a parameter λ. Here we show that λ suffers from extremely poor parameter recoverability in the accept-reject task. λ cannot be reliably estimated even for a simple version of prospect theory with linear probability weighting and value functions. λ cannot be reliably estimated even in impractically large experiments with participants subject to thousands of choices. The poor recoverability is driven by a trade-off between λ and the other model parameters. However, a measure derived from these parameters is extremely well recovered—and corresponds to estimating the area of gain-loss space in which people accept gambles. This area is equivalent to the number of gambles accepted in a given choice set. That is, simply counting accept decisions is extremely reliably recovered—but using prospect theory to make further use of exactly which gambles were accepted and which were rejected does not work.

scholarly journals Limiting probability measures

2020 ◽  
Vol 12 ◽  
Author(s):  
Irfan Alam
Keyword(s):  
Asymptotic Behavior ◽  
Classical Result ◽  
Nonstandard Analysis ◽  
High Dimensional ◽  
Probability Measures ◽  
Dimensional Sphere ◽  
Spherical Means ◽  
Fixed Direction ◽  
Set Up ◽  
Gaussian Moment

The coordinates along any fixed direction(s), of points on the sphere $S^{n-1}(\sqrt{n})$, roughly follow a standard Gaussian distribution as $n$ approaches infinity. We revisit this classical result from a nonstandard analysis perspective, providing a new proof by working with hyperfinite dimensional spheres. We also set up a nonstandard theory for the asymptotic behavior of integrals over varying domains in general. We obtain a new proof of the Riemann--Lebesgue lemma as a by-product of this theory. We finally show that for any function $f \co \mathbb{R}^k \to \mathbb{R}$ with finite Gaussian moment of an order larger than one, its expectation is given by a Loeb integral integral over a hyperfinite dimensional sphere. Some useful inequalities between high-dimensional spherical means of $f$ and its Gaussian mean are obtained in order to complete the above proof.

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