# The robustness of mean and variance approximations in pert and risk analysis

• 3.89 MB
• English
by
Loughborough University Business School , Loughborough, Leics
 ID Numbers Statement by D.G. Johnson. Series Loughborough University Business School research series -- 1997:4, Working paper / Logughborough University Business School -- 1997:4 Open Library OL16740840M ISBN 10 1859011241 OCLC/WorldCa 81248079

This paper examines further the problem of estimating the mean and variance of a continuous random variable from estimates of three points within the distr The problem arises most commonly in PERT and risk analysis where it can usually be assumed that the distribution in question is bell-shaped and positively skewed, often typified by a Beta by: This paper builds upon earlier work from the decision/risk analysis area in presenting simple, easy-to-use approximations for the mean and variance of PERT activity times.

These approximations offer significant advantages over the PERT formulas currently being taught and used, as well as over recently proposed by: In PERT analysis the activity time distribution is assumed to be a beta distribution, and the mean and variance of the activity time are estimated.

In PERT analysis the activity-time distribution is assumed to be a beta distribution, and the mean and variance of the activity time are estimated on the basis of the 'pessimistic', 'most likely.

Estimating the mean and variance 2 Traditional and Ginzburg’s PERT approximations Traditional PERT approximation Since in PERT applications aand b of the density function (1) are either known or subjectively determined, we can always transform the density function to a standard form, (1),0 1, 0, () () () () 1 − 1 Γ Γ Γ +File Size: 61KB.

In PERT analysis the activity time distribution is assumed to be a beta distribution, and the mean and variance of the activity time are estimated. The activity mean and variance are very useful. Revisiting the PERT mean and variance.

of skewness is the one that approximate the normal distribution which is also supported by PERT-Beta approximation Network Risk Analysis and PERT. Mean‐variance analysis is powerful for figuring out the optimal allocation of investments.

The framework is straightforward, as it uses mean, variance, and covariance of asset returns for finding the trade‐off between return and risk.

Instantaneous risk premia. The model in Eqs. – features four main instantaneous risk premia: A Diffusive Risk Premium (DRP), a Jump Risk Premium (JRP), a Variance Risk Premium (VRP), and a Long-run Mean Risk Premium (LRMRP), which are defined as DRP t = (γ 1 (1 − ρ 2) + γ 2 ρ) v t, JRP t = (g P − g Q) (λ 0 + λ 1 v t) VRP t = γ 2 σ v v t, LRMRP t = γ 3 σ m m t.

DRP is the. Chapter 4: Mean-Variance Analysis Modern portfolio theory identifies two aspects of the investment problem. First, an investor will want to maximize the expected rate of return on the portfolio.

### Description The robustness of mean and variance approximations in pert and risk analysis EPUB

Second, an investor will want to minimize the risk of the portfolio. The two aspects amount to the objective ofFile Size: KB. Downloadable. This paper builds upon earlier work from the decision/risk analysis area in presenting simple, easy-to-use approximations for the mean and variance of PERT activity times.

These approximations offer significant advantages over the PERT formulas currently being taught and used, as well as over recently proposed modifications. For instance, they are several orders of magnitude more. In classical PERT, the mean and variance were estimated to be 4 ˆ x 6 a mb µ ++ = and ()2 ˆ2 x 36 ba σ −.

A study by Farnum and Stanton revealed that the mean of the beta distribution in classical PERT is appropriate within some range of modal values, namely, a ba m b ba+ −.

It was shown that this parameter n has a great importance in the estimation of the time needed to complete the project which is essential in PERT methodology. In addition, by increasing n, the value of kurtosis increases and the variance decreases.

Therefore we can say that we obtain more accuracy and a greater likelihood of more extreme tail-area by: 6. PERT became part of Project Management literature after statistical and research findings. Historically 3-Point Estimate originated from PERT.

PERT was initially developed by US Navy to take care of scheduling uncertainties. The formula mentioned above is a close approximation of Mean found by Beta Distribution. Downloadable.

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as defined by the smooth model of decision making under ambiguity of Klibanoff, Marinacci and Mukerji ().

We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty.

Except for the constant variance assumption, the SGBC distribution satisfies the remainder of the assumptions for n = 3. Fig. 2 shows the kurtosis of the SGBC distribution compared with the SGBP, STSP and the beta PERT distributions.

Note that the SGBP(0,M,1,) and SGBC(0,M,1,3) distributions have a kurtosis close to 3 (which is the Gaussian kurtosis) when M ∈ (, ).Cited by: 3. Downloadable. The original PERT formulae  employ the mode and endpoints to estimate the mean and standard deviation of subjective probability distributions.

Though widely-used, they have met with criticism for their inaccuracy, and for their being limited to the beta distribution when there is no a priori reason why the distribution should be beta (, ). Discretization is a common decision analysis technique for which many methods are described in the literature and employed in practice.

The accuracy of these methods is typically judged by how well they match the mean, variance, and possibly higher moments of the Cited by: Mean-variance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk.

### Details The robustness of mean and variance approximations in pert and risk analysis EPUB

We describe in detail the interplay between objective and constraints in a number of single-period variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of by: Critical Path Analysis and PERT are powerful tools that help you to schedule and manage complex projects.

They were developed in the s to control large defense and technology projects, and have been used routinely since then. As with Gantt Charts, Critical Path Analysis (CPA) or the Critical Path Method (CPM) helps you to plan all tasks that must be completed as part of a project.

Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures. Related Databases. Derivative-free robust optimization by outer approximations.

### Download The robustness of mean and variance approximations in pert and risk analysis PDF

Mathematical Programming Robust Mean-Variance Hedging of Longevity Risk. Journal of Risk Cited by: Downloadable (with restrictions). We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as defined by the smooth model of decision making under ambiguity of Klibanoff, Marinacci and Mukerji ().

We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty. Abstract.

The mean-variance, or risk-return, approach to portfolio analysis is based upon the premise that the investor in allocating his wealth between different assets takes into account, not only the returns expected from alternative portfolio combinations, but also the risk attached to each such : Neil Thompson.

A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations Statistics & Probability Letters, Vol. 71, No. 4 Statistical dependence through common risk factors: With applications in uncertainty analysisCited by: (Mean and variance are poor performance measures for segmentation problems anyway; analyses of classiﬁcation errors are more appropriate .) Furthermore, strictly speaking we File Size: KB.

Your browser either does not support JAVA or has JAVA disabled. NAGARCH. Nonlinear Asymmetric GARCH(1,1) (NAGARCH) is a model with the specification: = + (− − −) + −, where ≥, ≥, > and (+) + variance process.

For stock returns, parameter is usually estimated to be positive; in this case, it reflects a phenomenon commonly referred to as the "leverage effect", signifying that negative. The main goal of the PERT analysis is to create a distribution of the project duration. According to PERT theory, the project duration follows a normal distribution, with the mean being the result of time analysis based on activity mean durations (x ¯) and the variance being equal to (4) σ PD 2 = ∑ x ∈ CP σ x 2 where σ PD 2 is the variance of the distribution of the project duration Cited by:   Finding Critical Path video: This video shows how to • Calculate expected times • Calculate variances • Calculate probability of.

Classical formulations of the portfolio optimization problem, such as mean-variance or Value-at-Risk (VaR) approaches, can result in a portfolio extremely sensitive to errors in the data, such as mean and covariance matrix of the returns. In this paper we propose a Cited by:. Downloadable!

Parameter uncertainty has been a recurrent subject treated in the financial literature. The normative portfolio selection approach considers two main kinds of decision rules: expected expected utility maximization and mean-variance criterion.

Assuming that the mean-variance criterion is a good approximation to the expected utility maximization paradigm, a major factor of concern.Publisher Summary. This chapter presents a new approach to portfolio optimization, which is called generalized mean-variance (GMV) analysis.

Mean-variance (MV) analysis is widely accepted as the best way of analyzing and explaining the benefits of diversification of holdings across a portfolio of assets at least in principal.TPM: Mean-Variance Approach Mathematical Analysis of the Minimum-Variance Opportunity Set Existence of a tangent portfolio Proposition If we have ﬁnitely many assets, and at least one asset has a mean which is not lower than the return Rf of the risk-free asset, then a tangent portfolio exists.

The proof can be found in the text book on page