Comment on “Aging Population, Retirement, and Risk Taking”

2020 ◽  
Vol 66 (6) ◽  
pp. 2792-2795 ◽  
Author(s):  
Rachel J. Huang ◽  
Larry Y. Tzeng ◽  
Jr-Yan Wang ◽  
Lin Zhao
Keyword(s):  
Risk Taking ◽  
Stochastic Dominance ◽  
Marginal Utility ◽  
Aging Population ◽  
Decision Makers ◽  
Terminal Wealth ◽  
Ranking Criterion ◽  
Log Normal ◽  
Necessary And Sufficient ◽  
Log Normal Distribution

Levy [Levy H (2016) Aging population, retirement, and risk taking. Management Sci. 62(5):1415–1430.] proposes asymptotic first-degree stochastic dominance (AFSD) as a distribution-ranking criterion for all nonsatiable decision makers with infinite investment horizons. By assuming that the terminal wealth follows a log-normal distribution and that the marginal utility is bounded, he offers the necessary and sufficient distributional condition for AFSD. Given Levy’s setting, we provide a counterexample to show that his condition is not necessary and offer the correct equivalent distributional condition for AFSD. This paper was accepted by Karl Diether, finance.

Comment on “Aging Population, Retirement, and Risk Taking”

2020 ◽  
Vol 66 (6) ◽  
pp. 2787-2791 ◽  
Author(s):  
Moshe Levy
Keyword(s):  
Lower Bound ◽  
Risk Taking ◽  
Marginal Utility ◽  
Geometric Mean ◽  
Aging Population ◽  
Economic Implication ◽  
Investment Horizon ◽  
Geometric Means ◽  
Economic Implications ◽  
Long Run

Levy [Levy H (2016) Aging population, retirement, and risk taking. Management Sci. 62(5):1415–1430] argues that the portfolio with the maximal geometric mean (MGM) asymptotically dominates any other portfolio; that is, as the investment horizon becomes very long, the MGM portfolio is preferred over any other portfolio for all preferences with marginal utility bounded from above, [Formula: see text]. The important economic implication is that in the long run, an all-equity portfolio dominates bond (or mixed) portfolios, which have lower geometric means. This comment shows that Levy’s result holds only if the marginal utility is also bounded from below. This seemingly technical correction has profound economic implications, because many commonly accepted preferences do not satisfy the lower bound condition. Indeed, for some standard preferences, the optimal stock–bond mix shifts toward bonds, not stocks, as the horizon increases, exactly opposite to Levy’s conclusion. This paper was accepted by Gustavo Manso, finance.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

scholarly journals Extreme geomagnetic activities: a statistical study

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Ryuho Kataoka
Keyword(s):  
Magnetic Storms ◽  
Magnetic Observatory ◽  
Statistical Distributions ◽  
Limited Data ◽  
Data Set ◽  
Sudden Commencements ◽  
The One ◽  
Log Normal ◽  
Geomagnetic Activities ◽  
Log Normal Distribution

Abstract Statistical distributions are investigated for magnetic storms, sudden commencements (SCs), and substorms to identify the possible amplitude of the one in 100-year and 1000-year events from a limited data set of less than 100 years. The lists of magnetic storms and SCs are provided from Kakioka Magnetic Observatory, while the lists of substorms are obtained from SuperMAG. It is found that majorities of events essentially follow the log-normal distribution, as expected from the random output from a complex system. However, it is uncertain that large-amplitude events follow the same log-normal distributions, and rather follow the power-law distributions. Based on the statistical distributions, the probable amplitudes of the 100-year (1000-year) events can be estimated for magnetic storms, SCs, and substorms as approximately 750 nT (1100 nT), 230 nT (450 nT), and 5000 nT (6200 nT), respectively. The possible origin to cause the statistical distributions is also discussed, consulting the other space weather phenomena such as solar flares, coronal mass ejections, and solar energetic particles.

scholarly journals UNIVERSAL STRUCTURE OF THE PERSONAL INCOME DISTRIBUTION

Fractals ◽  
2001 ◽  
Vol 09 (04) ◽  
pp. 463-470 ◽  
Author(s):  
WATARU SOUMA
Keyword(s):  
Income Distribution ◽  
Asset Price ◽  
Mean Value ◽  
High Income ◽  
Personal Income ◽  
Middle Income ◽  
The Mean ◽  
Universal Structure ◽  
Log Normal ◽  
Log Normal Distribution

We investigate the Japanese personal income distribution in the high income range over the 112 years (1887–1998), and that in the middle income range over the 44 years (1955–1998). It is observed that the distribution pattern of the log-normal with power law tail is the universal structure. However, the indexes specifying the distribution differ from year to year. One of the index characterizing the distribution is the mean value of the log-normal distribution; the mean income in the middle income range. It is found that this value correlates linearly with the gross domestic product (GDP). To clarify the temporal change of the equality or inequality of the distribution, we analyze Pareto and Gibrat indexes, which characterize the distribution in the high income range and that in the middle income range, respectively. It is found for some years that there is no correlation between the high income and the middle income. It is also shown that the mean value of Pareto index equals to 2, and the change of this index is effected by the change of the asset price. From these analysis, we derive four constraints that must be satisfied by mathematical models.

Numerical Simulation of Hopping Conductivity in Granular Metals

1990 ◽  
Vol 195 ◽  
Author(s):  
L. F. Chen ◽  
Ping Sheng ◽  
B. Abeles ◽  
M. Y. Zhou
Keyword(s):  
Cubic Lattice ◽  
Grain Sizes ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Straight Line ◽  
Disorder Potential ◽  
Effect Of Disorder ◽  
Log Normal ◽  
Hopping Conductance ◽  
Log Normal Distribution

ABSTRACTElectrical conduction in granular metals is simulated by mapping the hopping conductance between pairs of metal grains onto a simple cubic lattice with bonds between neighbors. By considering a log-normal distribution of grain sizes and the effect of disorder potential, the numerically calculated network conductance exhibit clear deviation from simple activation. Plotting -log a vs. T-½, where σ denotes conductivity and T the temperature, gives good straight line behavior with slopes comparable to those measured experimentally. Our results are noted to differ from those of Adkins et al.

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