On the fallacy of averages in project risk management

Managers recognize the presence of uncertainty in the estimates of the various parameters of their projects, but usually circumvent the required analysis (which can be demanding) by replacing the random variables by their averages. This paper argues against such practice. It demonstrates that gross errors can be committed in cost estimates and in the bids based on them.     

On optimal allocation of risk vectors

In this paper we extend results on optimal risk allocations for portfolios of real risks w.r.t. convex risk functionals to portfolios of risk vectors. In particular we characterize optimal allocations minimizing the total risk as well as Pareto optimal allocations. Optimal risk allocations are shown to exhibit a worst case dependence structure w.r.t. some specific max-correlation risk measure and they are comonotone w.r.t. a common worst case scenario measure. We also derive a new existence criterion for optimal risk allocations and discuss some examples.     

On optimal management of resources in distributed networks

In a network of processors, a distributed operating system must handle the management of shared resources. In this paper, it is shown how to solve this problem in using the model previously introduced in [1]. This model (interconnection of N Markov chains each representing locally a distributed process) allows us to prove the good functioning properties for some distributed problems such as the mutual exclusion problem and the deadlock problem, We also prove that fairness is a basic notion for setting the model’s parameters and obtain an optimal working of the network.     

Translation-invariant and positive-homogeneous risk measures and optimal portfolio management in the presence of a riskless component

Risk portfolio optimization, with translation-invariant and positive-homogeneous risk measures, leads to the problem of minimizing a combination of a linear functional and a square root of a quadratic functional for the case of elliptical multivariate underlying distributions.This problem was recently treated by the authors for the case when the portfolio does not contain a riskless component. When it does, however, the initial covariance matrix Σ becomes singular and the problem becomes more complicated. In the paper we focus on this case and provide an explicit closed-form solution of the minimization problem, and the condition under which this solution exists. The results are illustrated using data of 10 stocks from the NASDAQ Computer Index.     

On the optimal product mix in life insurance companies using conditional value at risk

This paper proposes a Conditional Value-at-Risk Minimization (CVaRM) approach to optimize an insurer’s product mix. By incorporating the natural hedging strategy of Cox and Lin (2007) and the two-factor stochastic mortality model of Cairns et al. (2006b), we calculate an optimize product mix for insurance companies to hedge against the systematic mortality risk under parameter uncertainty. To reflect the importance of required profit, we further integrate the premium loading of systematic risk. We compare the hedging results to those using the duration match method of Wang et al. (forthcoming), and show that the proposed CVaRM approach has a narrower quantile of loss distribution after hedging—thereby effectively reducing systematic mortality risk for life insurance companies.     

On the finiteness of optimal partitions

We prove that, under appropriate assumptions on the domain Ω and on the datumg, any optimal partition of Ω (minimizing the sum of the total perimeter and the approximation term is finite. Finiteness result for the problem of image segmentation in Artificial Vision can be deduced.

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Sunto Dimostriamo che, in opportune ipotesi sul dominio Ω e sul datog, ogni partizione ottimale di Ω (minimizzante il perimetro totale in Ω più il termine di approssimazione è finita. Se ne deducono risultati di finitezza per il problema della segmentazione di immagini in Visione Artificiale.

     

On the regularity of optimal controls

We outline some recent results on the regularity of optimal controls. We formulate the general regularity problem for open-loop and closed-loop controls, and explain how results for the open-loop case have implications for the closed-loop case as well. We then describe a number of results on the regularity of open-loop controls.Partially supported by a fellowship from the Alfred P. Sloan Foundation.Partially supported by NSF Grant No. DMS83-01678-01.     

On the existence of optimal controls

Using a recent result due to Berkovitz, we prove the existence of an optimal control in a broad class of problems, under relatively mild conditions.     

On the existence of optimal controls

A control process described by Eq. (1) is considered. Existence theorems for controls which minimize a functional of a general type are given by using weak compactness criteria.The authors are indebted to Professors R. Conti and L. D. Berkovitz for their helpful comments.     

On the optimal mapping of distributions

We consider the problem of mappingXY, whereX andY have given distributions, so as to minimize the expected value of X–Y². This is equivalent to finding the joint distribution of the random variable (X, Y), with specified marginal distributions forX andY, such that the expected value of X–Y² is minimized. We give a sufficient condition for the minimizing joint distribution and supply numerical results for two special cases.     

On a risk management analysis of oil spill risk using maritime transportation system simulation

Is it safer for New Orleans river gambling boats to be underway than to be dockside? Is oil transportation risk reduced by lowering wind restrictions from 45 to 35 knots at Hinchinbrook Entrance for laden oil tankers departing Valdez, Alaska? Should the International Safety Management (ISM) code be implemented fleet-wide for the Washington State Ferries in Seattle, or does it make more sense to invest in additional life craft? Can ferry service in San Francisco Bay be expanded in a safe manner to relieve high way congestion? These risk management questions were raised in a series of projects spanning a time frame of more than 10 years. They were addressed using a risk management analysis methodology developed over these years by a consortium of universities. In this paper we shall briefly review this methodology which integrates simulation of Maritime Transportation Systems (MTS) with incident/accident data collection, expert judgment elicitation and a consequence model. We shall describe recent advances with respect to this methodology in more detail. These improvements were made in the context of a two-year oil transportation risk study conducted from 2006?C2008 in the Puget Sound and surrounding waters. An application of this methodology shall be presented comparing the risk reduction effectiveness analysis of a one-way zone, an escorting and a double hull requirement in the same context.     

On optimal matchings

Givenn random red points on the unit square, the transportation cost between them is tipically √n logn.     

On optimal trees

The merits of different shapes of trees as data storage structures are compared. Given a tree data structure, the worst-case cost of searching the tree is studied, under weak assumptions about the cost of searches. In particular, it is assumed that the cost of a search path is the sum of the costs of the nodes on it, and that the cost of a node depends only on the outdegree of that node. The main results of the paper are that there are regular trees (as defined in the paper) which are nearly optimal among trees with a given number of nodes, and that minimal-cost trees are often nearly regular.     

A management oriented approach to reduce a project duration and its risk (variability)

The effects of different activities on risk and the expected completion time of a project are not the same; various activities have various effects on the successful completion of a project. Based on this fact, one of the most important issues in project management is to determine important activities and the amount of effort that should be assigned to control them, thereby completing the project successfully. In this paper, one index and one method are proposed to satisfy this necessity. Our main hypothesis is, expending effort on activities and controlling them actively results in activities risk reduction. Based on this hypothesis, the proposed index and method are compared to existing indices in the literature. Comparison results show that the proposed index and method strongly surpass other indices.     

On the local structure of optimal measures in the multi-marginal optimal transportation problem

We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension of the support of the solution.     

On the numerical determination of optimal inputs

The design of optimal inputs for linear and nonlinear system identification involves the maximization of a quadratic performance index subject to an input energy constraint. In the classical approach, a Lagrange multiplier is introduced whose value is an unknown constant. In recent papers, the Lagrange multiplier has been determined by plotting a curve of the Lagrange multiplier as a function of the critical interval length or a curve of input energy versus the interval length. A new approach is presented in this paper in which the Lagrange multiplier is introduced as a state variable and evaluated simultaneously with the optimal input. Numerical results are given for both a linear and a nonlinear dynamic system.     

On the optimal shape of magnetic swimmers

Magnetic actuation of elasto-magnetic devices has long been proposed as a simple way to propel fluid and achieve locomotion in environments dominated by viscous forces. Under the action of an oscillating magnetic field, a permanent magnet, when attached to an elastic tail, is able to generate bending waves and sufficient thrust for propulsion. We study the hydrodynamical effects of the magnetic head geometry using a geometrically exact formulation for the elastic tail elastohydrodynamics.We show that the spherical head geometry fails to take full advantage of the propulsive potential from the flexible tail. Nevertheless, while elongated prolate spheroids demonstrate a superior swimming performance, this is still regulated by the nature of the imposed magnetic field. Interestingly, the highest swimming speed is observed when the magnitude of the magnetic field is weak due to delays between the orientation of the magnetic moment and the oscillating magnetic field. This allows the stored elastic energy from the deformed tail to relax during the phase lag between the imposed magnetic field and the swimmer’s magnetic moment, favouring in this way the net propulsion. In particular, this result suggests the existence of optimal magnetic actuations that are non-smooth, and even discontinuous in time, in order to fully explore the propulsive potential associated with the relaxation dynamics of periodically deformed elastic filaments.     

On the duality between locally optimal tests and optimal experimental designs

Locally unbiased tests with maximal power curvature are determined as the solutions of an optimization problem which turns out to be of dual type as compared to the optimal design problem. In both cases the proper optimization problem is concerned with matrices only, and the transition from the matrix problem to the original variables is a separate second step. This approach provides a novel, statistical interpretation of the dual problem that arises with the optimal design problem.