scholarly journals Multiplicative Gains, Non-ergodic Utility, and the Just One More Paradox (with Supplemental Information)

2021 ◽  
Author(s):  
John K. Myers
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Expected Value ◽  
Multiplicative Semigroup ◽  
The Real ◽  
Operator Notation ◽  
Multiplicative Problems ◽  
Utility Preferences ◽  
Continuous Operators

Abstract Interest in multiplicative vs. additive returns on bets has been revived by Peters, who proposes ergodicity and added noise are useful in understanding utility preferences. Peters requires a Monte Carlo simulation to demonstrate empirically a supposed paradox that arithmetic expectation is inappropriate for multiplicative gain distribution forecasting. Here I formalize the r operator notation, which significantly simplifies multiplicative problems, as an extension of the arithmetic group's Δ/d discrete and continuous operators into the multiplicative semigroup. I show how the annihilating (absorbing) element of the multiplicative semigroup at 0, not +/-∞, may be used to conveniently represent nonlinear sequence occurrences, such as running out of money, without the need for special computer rules outside the mathematics. I use this to solve Peters' expected-value paradox elegantly, without ergodicities nor noise. But Peters misses the real paradox, called “Just One More”: the outcome of an advantageous additive gamble is identical to the outcome of a similar disadvantageous multiplicative gamble, after one trial; hence, by induction, an agent will keep playing. I propose games “Hero or Heroin” and “American Roulette” to highlight this paradox. This may help in explaining addiction. The Supplement contains further visualizations and arguments against the need and applicability of ergodics for utility. The results contribute to the understanding of repeated multiplicative gambles with annihilating states, and their utility.

scholarly journals Comparison of the Datar-Mathews Method and the Fuzzy Pay-Off Method through Numerical Results

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Mariia Kozlova ◽  
Mikael Collan ◽  
Pasi Luukka
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Simulation Model ◽  
Real Option ◽  
Fuzzy Numbers ◽  
Numerical Results ◽  
Option Valuation ◽  
The Real ◽  
Valuation Methods ◽  
Real Option Valuation

The paper compares numerically the results from two real option valuation methods, the Datar-Mathews method and the fuzzy pay-off method. Datar-Mathews method is based on using Monte Carlo simulation within a probabilistic valuation framework, while the fuzzy pay-off method relies on modeling the real option valuation by using fuzzy numbers in a possibilistic space. The results show that real option valuation results from the two methods seem to be consistent with each other. The fuzzy pay-off method is more robust and is also usable when not enough information is available for a construction of a simulation model.

scholarly journals Comparing the Thiessen’s Method against simpler alternatives using Monte Carlo Simulation

2018 ◽  
pp. 125-138
Author(s):  
Marcelo Guelfi ◽  
Carlos López-Vazquez
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Interval ◽  
Bootstrap Method ◽  
Field Measurements ◽  
Expected Value ◽  
Systematic Analysis ◽  
Sample Mean ◽  
Friedman's Test ◽  
Data Location

Estimating the expected value of a function over geographic areas is problem with a long history. In the beginning of the XX-th century the most common method was just the arithmetic mean of the field measurements ignoring data location. In 1911, Thiessen introduced a new weighting procedure measuring influence through an area and thus indirectly considering closeness between them. In another context, Quenouville created in 1949 the jackknife method which is used to estimate the bias and the standard deviation. In 1979 Efron invented the bootstrap method which, among other things, is useful to estimate the expected value and the confidence interval (CI) from a population. Although the Thiessen’s method has been used for more than 100 years, we were unable to find systematic analysis comparing its efficiency against the simple mean, or even to more recent methods like jackknife or boostrap. In this work we compared four methods to estimate de expected value.  Sample mean, Thiessen, the so called here jackknifed Thiessen and bootstrap. All of them are feasible for routine use in a network of fixed locations. The comparison was made using the Friedman’s Test after a Monte Carlo simulation. Two cases were taken for study: one analytic with three arbitrary functions and the other using experimental data from daily rain measured with a satellite. The results show that Thiessen’s method is the best estimator in almost all the cases with a 95% of confidence interval. Unlike the others, the last two considered methods supply a suitable CI, but the one obtained through jackknifed Thiessen was even more accurate, opening the door for future work.

scholarly journals Monte Carlo study of the frame, fluctuation and internal tensions of fluctuating membranes with fixed area

Soft Matter ◽  
2016 ◽  
Vol 12 (8) ◽  
pp. 2373-2380 ◽  
Author(s):  
Hayato Shiba ◽  
Hiroshi Noguchi ◽  
Jean-Baptiste Fournier
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lipid Membranes ◽  
Monte Carlo Study ◽  
Fluctuation Spectrum ◽  
Projected Area ◽  
Membrane Area ◽  
The Real ◽  
Lattice Monte Carlo ◽  
Fixed Area

Three types of surface tensions are investigated for lipid membranes using a lattice Monte Carlo simulation: the internal tension,σ, conjugated to the real membrane area, the mechanical frame tension,τ, conjugated to the projected area, and the “fluctuation tension”,r, obtained from the height fluctuation spectrum.

An Illusion of Spatial Hierarchy: Spatial Hierarchy in a Random Configuration

1996 ◽  
Vol 28 (9) ◽  
pp. 1533-1552 ◽  
Author(s):  
A Okabe ◽  
Y Sadahiro
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Real World ◽  
K Value ◽  
The Real ◽  
Spatial Hierarchy ◽  
Random Configuration

In this paper we show the properties of a spatial hierarchy found in a random configuration in which points are randomly placed on a plane and ranks are randomly assigned to these points. First we show a method of detecting a spatial hierarchy in a configuration of ranked points on a plane (not necessarily the random configuration). Second, using this method we obtain the spatial hierarchy of the random configuration mentioned above, and examine its properties theoretically as well as numerically with the Monte Carlo simulation. From this examination, we find that the spatial hierarchy of the random configuration shares more or less similar properties with Christaller's spatial hierarchy. Stated explicitly, the shape of dominant regions is hexagonal on average; the areas of the same rank centers are fairly homogeneous; the K value defined by Christaller is almost constant. The constant K of the random configuration is close to seven, implying that the spatial hierarchy of the random configuration is close to Christaller's hierarchy of the administrative principle. These results explain to a certain extent why spatial hierarchies are often observed in the real world. At the same time, these results give us a warning. Even if we find a spatial hierarchy in the real world, we should question whether or not the observed hierarchy is a seeming hierarchy like the spatial hierarchy in the random configuration.

scholarly journals A Monte Carlo simulation to validate the EAR cut-point method for assessing the prevalence of nutrient inadequacy at the population level

2004 ◽  
Vol 7 (7) ◽  
pp. 893-900 ◽  
Author(s):  
B de Lauzon ◽  
JL Volatier ◽  
A Martin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Population Level ◽  
Point Method ◽  
Probabilistic Methods ◽  
Recommended Dietary Allowance ◽  
The Real ◽  
Cut Point ◽  
Probability Approach ◽  
Dietary Allowance

AbstractObjective:The aim of this study was to validate the EAR cut-point method for assessing the prevalence of nutrient inadequacy at the population level.Design and subjects:Different methods for estimating the prevalence of inadequate intake were compared: the cut-off point method, with cut-off points at the Recommended Dietary Allowance (RDA), 0.66 RDA, 0.50 RDA and the Estimated Average Requirement (EAR); the probability approach; and a Monte Carlo simulation. In total, 591 men and 674 women, aged 20–55 years, were included in the analyses.Results:The prevalence of inadequate intake as estimated by the EAR cut-point method was similar to the prevalence of inadequacy estimated by both probabilistic methods. The cut-point method with RDA, 0.66 RDA and 0.50 RDA as cut-off limits induced an over- or an underestimation of the real prevalence of inadequacy.Conclusions:Probabilistic methods consider both the intake variability and the requirement variability, and, as a result, their estimation should be closer to the real prevalence of inadequacy. The use of the EAR cut-point method yields a good estimation of the prevalence of inadequate intake, comparable to the probability approach, and limits over- and underestimation of the prevalence induced by other cut-off points.

scholarly journals QUANTITATIVE DECISION MAKING IN LAND BANKING: A MONTE CARLO SIMULATION FOR CHINA'S REAL ESTATE DEVELOPERS

2012 ◽  
Vol 16 (4) ◽  
pp. 355-369 ◽  
Author(s):  
Haijun Bao ◽  
Alain Yee-Loong Chong ◽  
Hongdi Wang ◽  
Liyuan Wang ◽  
Yikun Huang
Keyword(s):  
Decision Making ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Real Estate ◽  
Decision Model ◽  
Real Estate Industry ◽  
The Real ◽  
The Real Estate ◽  
Land Banking ◽  
Future Developments

The real estate industry is one of the fast growing industries in many developing countries such as China and India. The Chinese real estate industry has gone through many reforms from offering housing as part of its social welfare system, to the current capitalist model based on demand and supply. Due to these reforms and the shortage of lands for development in China's urban cities, many Chinese property firms have resorted to land banking in order to secure land property for future developments. However, in China, land speculation is considered illegal, while failure to purchase the suitable land for future developments will hinder the real estate developers’ future business and growth. The purpose of this paper is to develop a decision making model for property developments in their land banking decisions and strategies. The paper employed mathematical modeling and Monte Carlo simulation to examine our decision model, and further validated our results by conducting the simulation by using China Vanke Co. Ltd as a case study. This study is one of the first few studies that develop a decision model for land banking in China. It also helps real estate enterprises to make rational and dynamic decision in the current dynamic property market.

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