Explore the vast range of titles available.

In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ -divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on φ -divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with φ -divergence uncertainty is tractable for most of the choices of φ typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach. This paper was accepted by Gérard P. Cachon, optimization.

IntroductionEliminating acute malnutrition in children under 5 years of age stands as a critical health priority outlined in the United Nations Sustainable Development Goal 2, ‘Zero Hunger’. This requires targeted provision of treatment and preventative services. However, accurately forecasting future prevalence of cases remains challenging, with the application of predictive models being notably scarce. Addressing this gap, this paper aims to identify factors associated with Global Acute Malnutrition (GAM) and explores the potential of machine learning in predicting its prevalence using data from Somalia.MethodsSurvey data on GAM prevalence systematically collected in Somalia every 6 months at a district level from 2017 to 2021 were collated alongside a range of potential climatic, demographic, disease, environmental, conflict and food security-related factors over a matching time period. We conducted both simple and multiple, parametric and non-parametric statistical analyses to identify factors associated with GAM to be used as input in forecasting future GAM prevalence. We then applied tree-based machine learning algorithms to a dataset comprising the GAM prevalence estimates and associated factors to try to forecast the trajectory and fluctuations in GAM prevalence 6 months into the future.ResultsWe found factors statistically associated with GAM prevalence relating to rainfall, land vegetation quality, food security status, crop production and demographics. The majority of these associations were nonlinear, motivating the use of tree-based machine learning–based forecasts. Among the forecasting methods tested, random forest machine learning proves to be the most effective and was found to accurately forecast the direction of GAM prevalence in test data for many of the districts in Somalia.

Background National projections of life expectancy are made periodically by statistical offices or actuarial societies in Europe and are widely used, amongst others for reforms of pension systems. However, these projections may not provide a good estimate of the future trends in life expectancy of different social-economic groups. The objective of this study is to provide insight in future trends in life expectancies for low, mid and high educated men and women living in the Netherlands. Methods We used a three-layer Li and Lee model with data from neighboring countries to complement Dutch time series. Results Our results point at further increases of life expectancy between age 35 and 85 and of remaining life expectancy at age 35 and age 65, for all education groups in the Netherlands. The projected increase in life expectancy is slightly larger among the high educated than among the low educated. Life expectancy of low educated women, particularly between age 35 and 85, shows the smallest projected increase. Our results also suggest that inequalities in life expectancies between high and low educated will be similar or slightly increasing between 2018 and 2048. We see no indication of a decline in inequality between the life expectancy of the low and high educated. Conclusions The educational inequalities in life expectancy are expected to persist or slightly increase for both men and women. The persistence and possible increase of inequalities in life expectancy between the educational groups may cause equity concerns of increases in pension age that are equal among all socio-economic groups.

Objective We investigate whether there are changes over time in years in good health people can expect to live above (surplus) or below (deficit) the pension age, by level of attained education, for the past (2006), present (2018) and future (2030) in the Netherlands. Methods We used regression analysis to estimate linear trends in prevalence of four health indicators: self-assessed health (SAH), the Organization for Economic Co-operation and Development (OECD) functional limitation indicator, the OECD indicator without hearing and seeing, and the activities-of-daily-living (ADL) disability indicator, for individuals between 50 and 69 years of age, by age category, gender and education using the Dutch National Health Survey (1989–2018). We combined these prevalence estimates with past and projected mortality data to obtain estimates of years lived in good health. We calculated how many years individuals are expected to live in good health above (surplus) or below (deficit) the pension age for the three points in time. The pension ages used were 65 years for 2006, 66 years for 2018 and 67.25 years for 2030. Results Both for low educated men and women, our analyses show an increasing deficit of years in good health relative to the pension age for most outcomes, particularly for the SAH and OECD indicator. For high educated we find a decreasing surplus of years lived in good health for all indicators with the exception of SAH. For women, absolute inequalities in the deficit or surplus of years in good health between low and high educated appear to be increasing over time. Conclusions Socio-economic inequalities in trends of mortality and the prevalence of ill-health, combined with increasing statutory pension age, impact the low educated more adversely than the high educated. Policies are needed to mitigate the increasing deficit of years in good health relative to the pension age, particularly among the low educated.

Two effects largely determine global warming: the well-known greenhouse effect and the less well-known solar radiation effect. An increase in concentrations of carbon dioxide and other greenhouse gases contributes to global warming: the greenhouse effect. In addition, small particles, called aerosols, reflect and absorb sunlight in the atmosphere. More pollution causes an increase in aerosols, so that less sunlight reaches the Earth (global dimming). Despite its name, global dimming is primarily a local (or regional) effect. Because of the dimming the Earth becomes cooler: the solar radiation effect. Global warming thus consists of two components: the (global) greenhouse effect and the (local) solar radiation effect, which work in opposite directions. Only the sum of the greenhouse effect and the solar radiation effect is observed, not the two effects separately. Our purpose is to identify the two effects. This is important, because the existence of the solar radiation effect obscures the magnitude of the greenhouse effect. We propose a simple climate model with a small number of parameters. We gather data from a large number of weather stations around the world for the period 1959-2002. We then estimate the parameters using dynamic panel data methods, and quantify the parameter uncertainty. Next, we decompose the estimated temperature change of 0.73°C (averaged over the weather stations) into a greenhouse effect of 1.87°C, a solar radiation effect of—1.09°C, and a small remainder term. Finally, we subject our findings to extensive sensitivity analyses.

The vast literature on extrapolative stochastic mortality models focuses mainly on the extrapolation of past mortality trends and summarizes the trends by one or more latent factors. However, the interpretation of these trends is typically not very clear. On the other hand, explanation methods are trying to link mortality dynamics with observable factors. This serves as an intermediate step between the two methods. We perform a comprehensive analysis on the relationship between the latent trend in mortality dynamics and the trend in economic growth represented by gross domestic product (GDP). Subsequently, the Lee-Carter framework is extended through the introduction of GDP as an additional factor next to the latent factor, which provides a better fit and better interpretable forecasts.

In optimization problems appearing in fields such as economics, finance, or engineering, it is often important that a risk measure of a decision-dependent random variable stays below a prescribed level. At the same time, the underlying probability distribution determining the risk measure's value is typically known only up to a certain degree and the constraint should hold for a reasonably wide class of probability distributions. In addition, the constraint should be computationally tractable. In this paper we review and generalize results on the derivation of tractable counterparts of such constraints for discrete probability distributions. Using established techniques in robust optimization, we show that the derivation of a tractable robust counterpart can be split into two parts, one corresponding to the risk measure and the other to the uncertainty set. This holds for a wide range of risk measures and uncertainty sets for probability distributions defined using statistical goodness-of-fit tests or probability metrics. In this way, we provide a unified framework for reformulating this class of constraints, extending the number of solvable risk measure-uncertainty set combinations considerably, also including risk measures that are nonlinear in the probabilities. To provide a clear overview for the user, we provide the computational tract ability status for each of the uncertainty set-risk measure pairs, some of which have been solved in the literature. Examples, including portfolio optimization and antenna array design, illustrate the proposed approach in a theoretical and numerical setting.

In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the 1972 result of Ben-Tal and Hochman (BH) in which tight upper and lower bounds on the expectation of a convex function of a random variable are given. First, we use these results to treat ambiguous expected feasibility constraints to obtain exact reformulations for both functions that are convex and concave in the components of the random variable. This approach requires, however, the independence of the random variables and, moreover, may lead to an exponential number of terms in the resulting robust counterparts. We then show how upper bounds can be constructed that alleviate the independence restriction, and require only a linear number of terms, by exploiting models in which random variables are linearly aggregated. Moreover, using the BH bounds we derive three new safe tractable approximations of chance constraints of increasing computational complexity and quality. In a numerical study, we demonstrate the efficiency of our methods in solving stochastic optimization problems under mean-MAD ambiguity. The electronic companion is available at https://doi.org/10.1287/opre.2017.1688 .

We empirically compare a wide range of term structure models used in the pricing and, in particular, hedging of caps and swaptions. We analyze the influence of the number of factors on the hedging and pricing results, and investigate the type of data—interest rate or derivative price—in combination with the estimation technique that should be used to obtain the best hedging and pricing results. We use data on interest rates, and cap and swaption prices from 1995–1999. The empirical results show that, if the number of hedge instruments is equal to the number of factors, multi-factor models outperform one-factor models in hedging caps and swaptions. However, if one uses a large set of hedge instruments, one-factor models perform as well as multi-factor models. We find that models with two or three factors imply better out-of-sample predictions of cap and swaption prices than one-factor models. Estimation on the basis of current derivative prices leads to more accurate out-of-sample prediction of cap and swaption prices than estimation on the basis of interest rate data.

Parameter uncertainty and model misspecification can have a significant impact on the performance of hedging strategies for longevity risk. To mitigate this lack of robustness, we propose an approach in which the optimal hedge is determined by optimizing the worst-case value of the objective function with respect to a set of plausible probability distributions. In the empirical analysis, we consider an insurer who hedges longevity risk using a longevity bond, and we compare the worst-case (robust) optimal hedges with the classical optimal hedges in which parameter uncertainty and model misspecification are ignored. We find that unless the risk premium on the bond is close to zero, the robust optimal hedge is significantly less sensitive to variations in the underlying probability distribution. Moreover, the robust optimal hedge on average outperforms the nominal optimal hedge unless the probability distribution used by the nominal hedger is close to the true distribution.