scholarly journals A possibilistic and probabilistic approach to precautionary saving

2017 ◽  
Vol 64 (3) ◽  
pp. 273-295 ◽  
Author(s):  
Irina Georgescu ◽  
Adolfo Cristóbal-Campoamor ◽  
Ana Lucia-Casademunt
Keyword(s):  
Fuzzy Number ◽  
Mixed Models ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Precautionary Saving ◽  
Optimal Choice ◽  
Background Risk ◽  
Precautionary Savings ◽  
Income Risk ◽  
Optimal Saving

This paper proposes two mixed models to study a consumer?s optimal saving in the presence of two types of risk: income risk and background risk. In the first model, income risk is represented by a fuzzy number and background risk by a random variable. In the second model, income risk is represented by a random variable and background risk by a fuzzy number. For each model, three notions of precautionary savings are defined as indicators of the extra saving induced by income and background risk on the consumer?s optimal choice. In conclusion, we can characterize the conditions that allow for extra saving relative to optimal saving under certainty, even when a certain component of risk is modelled using fuzzy numbers.

scholarly journals The Effect of Prudence on the Optimal Allocation in Possibilistic and Mixed Models

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 133 ◽  
Author(s):  
Irina Georgescu
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Fuzzy Number ◽  
Mixed Models ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
Random Variables ◽  
Background Risk ◽  
Investment Risk ◽  
Approximate Formulas

In this paper, several portfolio choice models are studied: a purely possibilistic model in which the return of the risky is a fuzzy number, and four models in which the background risk appears in addition to the investment risk. In these four models, risk is a bidimensional vector whose components are random variables or fuzzy numbers. Approximate formulas of the optimal allocation are obtained for all models, expressed in terms of some probabilistic or possibilistic moments, depending on the indicators of the investor preferences (risk aversion, prudence).

scholarly journals Dynastic Precautionary Savings

2021 ◽  
Author(s):  
Corina Boar
Keyword(s):  
Panel Study ◽  
Precautionary Saving ◽  
Permanent Income ◽  
Precautionary Savings ◽  
Income Dynamics ◽  
Income Risk ◽  
Income Uncertainty ◽  
Parent Child

Abstract This article documents that parents accumulate savings to insure their children against income risk. I refer to this behaviour as dynastic precautionary saving. Using a sample of matched parent–child pairs from the Panel Study of Income Dynamics, I test for dynastic precautionary savings by examining the response of parental consumption to the child’s permanent income uncertainty. I exploit variation in permanent income risk across age and industry–occupation groups to confirm that, all else equal, higher uncertainty in the child’s permanent income depresses parental consumption, indicating a precautionary saving motive across generations.

An Assessment of Non-Intrusive Probabilistic Methods for Turbomachinery Problems

2010 ◽  
Author(s):  
Sriram Shankaran ◽  
Brian Barr ◽  
Ramakrishna Mallina ◽  
Ravikanth Avancha ◽  
Alex Stein
Keyword(s):  
Monte Carlo ◽  
Performance Measures ◽  
Performance Metrics ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Optimal Choice ◽  
Probabilistic Methods ◽  
Probabilistic Algorithms ◽  
Optimal Basis ◽  
The Impact

The ability to quantify the impact of uncertainty on performance is an important facet of engineering design. Computational Fluid Dynamics (CFD) studies during the design cycle typically utilize estimates of boundary conditions, geometry and model constants, all of which have uncertainty that could lead to variations in the estimated performance of the design. Traditionally, engineering environments have relied on Monte-Carlo (MC) simulations to obtain probabilistic estimates. But MC methods have poor convergence rate leading to prohibitive computational requirements when used in conjunction with medium to high fidelity computational tools. In this study, we will use an alternate probabilistic approach. We assume that the uncertainties in our computational system can be modeled as random variables with known/prescribed distributions, use CFD solvers to estimate the performance measures and then use a psuedo-spectral probabilistic collocation technique to determine regression/interpolation fits. The psuedo-spectral discrete expansion uses the orthogonal polynomials from the Askey-Wiener basis and finds the coefficients of the expansion [1]. We will restrict our attention to problems with one random variable and hence can without ambiguity choose the Gauss quadratures as the optimal choice to obtain statistical data (mean, variance, moments etc.) of the performance measures. The computational frame-work will be first validated against Monte-Carlo simulations to assess convergence of pdfs. It will then be used to assess the variability in compressor blade efficiency and turbine vane loss due to uncertainty in inflow conditions. The results will be used to answer the following questions. Do we need new probabilistic algorithms to quantify the impact of uncertainty? What is the optimal basis for standard performance metrics in turbomachinery? What are the computational and accuracy requirements of this probabilistic approach? Are there alternate (more efficient) techniques? We believe that the answers to the above questions will provide a quantitative basis to assess the usefulness of non-intrusive (and possibly intrusive) probabilistic methods to analyze variability in engineering designs.

scholarly journals Optimal Prevention with Possibilistic and Mixed Background Risk

2018 ◽  
Vol 14 (01) ◽  
pp. 21-35
Author(s):  
Irina Georgescu ◽  
Ana María Lucia Casademunt
Keyword(s):  
Mixed Models ◽  
Sufficient Conditions ◽  
Background Risk ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Optimal Saving

In this paper, the effect of posibilistic or mixed background risk on the level of optimal prevention is studied. In the framework of five purely possibilistic or mixed models, necessary and sufficient conditions are found such that the level of optimal saving decreases or increases as a result of the actions of various types of background risk. This way our results complete those obtained by Courbage and Rey for some prevention models with probabilistic background risk.

scholarly journals 222 Partitioning of retained energy between protein and fat gain, and heat of product formation and support metabolism in growing beef cattle

2020 ◽  
Vol 98 (Supplement_4) ◽  
pp. 158-158
Author(s):  
Phillip A Lancaster
Keyword(s):  
Linear Regression ◽  
Mixed Models ◽  
Multivariate Regression ◽  
Literature Search ◽  
Energy Use ◽  
Random Variable ◽  
Product Formation ◽  
Metabolizable Energy ◽  
Overall Efficiency ◽  
Metabolizable Energy Intake

Abstract Multiple linear regression inaccurately computes the efficiency of energy use for protein and fat gain. The objective was to quantify efficiency of metabolizable energy use for protein and fat gain along with heats of product formation and support metabolism. A literature search was performed to compile data (31 studies, 214 treatment means) on metabolizable energy intake (MEI) and composition of empty body gain in growing steers and heifers. Data analyses were performed using R statistical package for mixed models with study as random variable. Linear regression of MEI on energy gain (EG; P < 0.001; R2 = 0.627) resulted in an estimate of metabolizable energy for maintenance (MEm) of 156 kcal/kg.75 and efficiency of ME use for gain of 0.518. Linear regression of MEI on EG as protein and fat (P < 0.001; R2 = 0.623) resulted in an estimate of MEm of 149 kcal/kg.75, and efficiency of protein (kp) and fat (kf) gain of 0.274 and 0.585, respectively, resulting in an overall efficiency of EG of 0.520. Nonlinear regression model (EG = kg*(MEI-MEm)) resulted in an estimate of MEm of 103 kcal/kg.75 and efficiency of EG of 0.342. The heat of product formation was assumed to be 0.48 (1 – 0.52) and the heat of support metabolism (HiEv) 0.18 (0.52 – 0.34). Multivariate regression was used to fit simultaneous models for EG as protein (EGp = (kp+HiEvp)*k*MEA) and fat (EGf = (kf+(0.18-HiEvp))*(1-k)*MEA). Estimates (P < 0.001) of kp and kf were 0.12 ± 0.01 and 0.63 ± 0.02, and HiEvp and proportion of ME available for protein gain (k) were 0.11 ± 0.01 and 0.75 ± 0.01, respectively. The heat of product formation and support metabolism for protein were 0.77 and 0.11, and fat were 0.30 and 0.07, respectively. In conclusion, efficiency of ME use for protein was lesser than for fat gain, and heat of support metabolism was greater for protein than fat gain.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

scholarly journals A Method for the Statistical Evaluation of Crosstalk Effect Between Three Parallel Conductors

1999 ◽  
Vol 22 (2) ◽  
pp. 111-119
Author(s):  
P. T. Trakadas ◽  
C. N. Capsalis
Keyword(s):  
Closed Form ◽  
Uniform Distribution ◽  
Transmission Lines ◽  
Statistical Evaluation ◽  
Unit Length ◽  
Surrounding Medium ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Mutual Inductance ◽  
Theoretical Results

There are several cases at which, in order to evaluate the crosstalk effect among transmission lines carrying useful signals, there is a need for probabilistic approach. This paper considers the problem of crosstalk estimation between transmission lines consisting of three conductors in a homogeneous surrounding medium, where the distance between the conductors is a random variable described by uniform distribution. The transmission lines are considered as electrically short. A closed-form equation is developed for the statistical distribution of the per-unit-length mutual inductance(lm)and an analytical one is described for the evaluation of the per-unit-length capacitance(cm). Theoretical results are compared with simulated ones for validation purposes.

scholarly journals Precautionary Savings, Illiquid Assets, and the Aggregate Consequences of Shocks to Household Income Risk

Econometrica ◽  
2019 ◽  
Vol 87 (1) ◽  
pp. 255-290 ◽  
Author(s):  
Christian Bayer ◽  
Ralph Luetticke ◽  
Lien Pham-Dao ◽  
Volker Tjaden
Keyword(s):  
Household Income ◽  
Precautionary Savings ◽  
Income Risk ◽  
Illiquid Assets

scholarly journals On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 79 ◽  
Author(s):  
Vadim Semenikhine ◽  
Edward Furman ◽  
Jianxi Su
Keyword(s):  
Risk Model ◽  
Tail Dependence ◽  
Random Variable ◽  
Copula Function ◽  
Background Risk ◽  
Aggregate Risk ◽  
Multivariate Gamma Distribution ◽  
Multivariate Probability Distribution ◽  
Dependent Risks ◽  
Main Message

One way to formulate a multivariate probability distribution with dependent univariate margins distributed gamma is by using the closure under convolutions property. This direction yields an additive background risk model, and it has been very well-studied. An alternative way to accomplish the same task is via an application of the Bernstein–Widder theorem with respect to a shifted inverse Beta probability density function. This way, which leads to an arguably equally popular multiplicative background risk model (MBRM), has been by far less investigated. In this paper, we reintroduce the multiplicative multivariate gamma (MMG) distribution in the most general form, and we explore its various properties thoroughly. Specifically, we study the links to the MBRM, employ the machinery of divided differences to derive the distribution of the aggregate risk random variable explicitly, look into the corresponding copula function and the measures of nonlinear correlation associated with it, and, last but not least, determine the measures of maximal tail dependence. Our main message is that the MMG distribution is (1) very intuitive and easy to communicate, (2) remarkably tractable, and (3) possesses rich dependence and tail dependence characteristics. Hence, the MMG distribution should be given serious considerations when modelling dependent risks.

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