The liner shipping berth scheduling problem with transit times

In this paper speed optimization of an existing liner shipping network is solved by adjusting the port berth times. The objective is to minimize fuel consumption while retaining the customer transit times including the transhipment times. To avoid too many changes to the time table, changes of port berth times are only accepted if they lead to savings above a threshold value. Since the fuel consumption of a vessel is a non-linear convex function of the speed, it is approximated by a piecewise linear function. The developed model is solved using exact methods in less than two minutes for large instances. Computational experiments on real-size liner shipping networks are presented showing that fuels savings in the magnitude 2–10% can be obtained. The work has been carried out in collaboration with Maersk Line and the tests instances are confirmed to be representative of real-life networks.     

A stochastic programming approach for floods emergency logistics

This article presents a model to assist decision makers in the logistics of a flood emergency. The model attempts to optimize inventory levels for emergency supplies as well as vehicles’ availability, in order to deliver enough supplies to satisfy demands with a given probability. A spatio-temporal stochastic process represents the flood occurrence. The model is approximately solved with sample average approximation. The article presents a method to quantify the impact of the various intervening logistics parameters. An example is provided and a sensitivity analysis is performed. The studied example shows large differences between the impacts of logistics parameters such as number of products, number of periods, inventory capacity and degree of demand fulfillment on the logistics cost and time. This methodology emerges as a valuable tool to help decision makers to allocate resources both before and after a flood occurs, with the aim of minimizing the undesirable effects of such events.     

Modern Likelihood‐Frequentist Inference

We offer an exposition of modern higher order likelihood inference and introduce software to implement this in a quite general setting. The aim is to make more accessible an important development in statistical theory and practice. The software, implemented in an R package, requires only that the user provide code to compute the likelihood function and to specify extra‐likelihood aspects of the model, such as stopping rule or censoring model, through a function generating a dataset under the model. The exposition charts a narrow course through the developments, intending thereby to make these more widely accessible. It includes the likelihood ratio approximation to the distribution of the maximum likelihood estimator, that is the p^? formula, and the transformation of this yielding a second‐order approximation to the distribution of the signed likelihood ratio test statistic, based on a modified signed likelihood ratio statistic r^?. This follows developments of Barndorff‐Nielsen and others. The software utilises the approximation to required Jacobians as developed by Skovgaard, which is included in the exposition. Several examples of using the software are provided.     

A PRIMAL–DUAL ALGORITHM FOR BSDES

We generalize the primal–dual methodology, which is popular in the pricing of early‐exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dynamic program, which was precomputed, e.g., by least‐squares Monte Carlo, this methodology enables us to construct a confidence interval for the unknown true solution of the time‐discretized (reflected) BSDE at time 0. We numerically demonstrate the practical applicability of our method in two 5‐dimensional nonlinear pricing problems where tight price bounds were previously unavailable.     

PRICING SWAPTIONS UNDER MULTIFACTOR GAUSSIAN HJM MODELS

Several approximations have been proposed in the literature for the pricing of European‐style swaptions under multifactor term structure models. However, none of them provides an estimate for the inherent approximation error. Until now, only the Edgeworth expansion technique of Collin‐Dufresne and Goldstein is able to characterize the order of the approximation error. Under a multifactor HJM Gaussian framework, this paper proposes a new approximation for European‐style swaptions, which is able to set bounds on the magnitude of the approximation error and is based on the conditioning approach initiated by Curran and Rogers and Shi. All the proposed pricing bounds will arise as a simple by‐product of the Nielsen and Sandmann setup, and will be shown to provide a better accuracy–efficiency trade‐off than all the approximations already proposed in the literature.     

On Goodness of Fit for Operational Risk

The Advanced Measurement Approach (AMA) to operational risk, as described by the Basel Committee on Banking Supervision ( 2011 ), provides a framework meant to be used by banks for establishing the capital required to be set aside to cover worst‐case operational loss scenarios. The problems raised by an AMA approach are primarily statistical in nature, and many lie at the frontier of statistical research. The aim of this paper is to contribute to one of the more pressing challenges of an AMA, namely that of testing the goodness of fit (GoF) of a distributional family to operational loss data. Our focus is on extending certain classically known tests, such as that of Anderson–Darling, with particular emphasis on the right tails of the distributions. The nature of such GoF tests is examined in detail, and computational efficiency of the procedures is taken into account. We also propose a novel saddlepoint approximation method for assessing the asymptotic null distributions of the test statistics based on the eigenvalues of covariance kernels estimated via a jackknife and influence function‐based approach.     

Government debt and optimal monetary and fiscal policy

How do different levels of government debt affect the optimal conduct of monetary and fiscal policies? And what do these optimal policies imply for the evolution of government debt over time? To provide an answer, this paper studies a standard monetary policy model with nominal rigidities and monopolistic competition and adds to it a fiscal authority that issues nominal non-state contingent debt, levies distortionary labor income taxes and determines the level of public goods provision. Higher government debt levels make it optimal to reduce public spending, so as to dampen the adverse incentive effects of distortionary taxes, but also strongly influence the optimal stabilization response following technology shocks. In particular, higher debt levels give rise to larger risks to the fiscal budget and to tax rates. This makes it optimal to reduce government debt over time. The optimal speed of debt reduction is missed when using first-order approximations to optimal policies, but is shown to be quantitatively significant in a second-order approximation, especially when technology movements are largely unpredictable in nature.     

Combining kernel estimators in the uniform deconvolution problem

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative. Initially the inversions yield two different estimators of the density and two estimators of the distribution function. We construct asymptotically optimal convex combinations of these two estimators. We also derive pointwise asymptotic normality of the resulting estimators, the pointwise asymptotic biases and an expansion of the mean integrated squared error of the density estimator. It turns out that the pointwise limit distribution of the density estimator is the same as the pointwise limit distribution of the density estimator introduced by Groeneboom and Jongbloed (Neerlandica, 57, 2003, 136), a kernel smoothed nonparametric maximum likelihood estimator of the distribution function.     

Risk management in liner ship fleet deployment: A joint chance constrained programming model

This paper provides a tangible methodology to deal with the liner ship fleet deployment problem aiming at minimizing the total cost while maintaining a service level under uncertain container demand. The problem is first formulated as a joint chance constrained programming model, and the sample average approximation method and mixed-integer programming are used to deal with it. Finally, a numerical example of a liner shipping network is carried out to verify the applicability of the proposed model and solution algorithm. It is found that the service level has significant effect on the total cost.