Optimal designs for multivariate logistic mixed models with longitudinal data

This paper considers the optimal design problem for multivariate mixed-effects logistic models with longitudinal data. A decomposition method of the binary outcome and the penalized quasi-likelihood are used to obtain the information matrix. The D-optimality criterion based on the approximate information matrix is minimized under different cost constraints. The results show that the autocorrelation coefficient plays a significant role in the design. To overcome the dependence of the D-optimal designs on the unknown fixed-effects parameters, the Bayesian D-optimality criterion is proposed. The relative efficiencies of designs reveal that both the cost ratio and autocorrelation coefficient play an important role in the optimal designs.     

Minimally informative distributions with given rank correlation for use in uncertainty analysis

Minimum information bivariate distributions with uniform marginals and a specified rank correlation are studied in this paper. These distributions play an important role in a particular way of modeling dependent random variables which has been used in the computer code UNICORN for carrying out uncertainty analyses. It is shown that these minimum information distributions have a particular form which makes simulation of conditional distributions very simple. Approximations to the continuous distributions are discussed and explicit formulae are determined. Finally a relation is discussed to DAD theorems, and a numerical algorithm is given (which has geometric rate of covergence) for determining the minimum information distributions.     

Books on probability ideas are reviewed

In this paper, semiparametric methods are applied to estimate multivariate volatility functions, using a residual approach as in [J. Fan and Q. Yao, Efficient estimation of conditional variance functions in stochastic regression, Biometrika 85 (1998), pp. 645–660; F.A. Ziegelmann, Nonparametric estimation of volatility functions: The local exponential estimator, Econometric Theory 18 (2002), pp. 985–991; F.A. Ziegelmann, A local linear least-absolute-deviations estimator of volatility, Comm. Statist. Simulation Comput. 37 (2008), pp. 1543–1564], among others. Our main goal here is two-fold: (1) describe and implement a number of semiparametric models, such as additive, single-index and (adaptive) functional-coefficient, in volatility estimation, all motivated as alternatives to deal with the curse of dimensionality present in fully nonparametric models; and (2) propose the use of a variation of the traditional cross-validation method to deal with model choice in the class of adaptive functional-coefficient models, choosing simultaneously the bandwidth, the number of covariates in the model and also the single-index smoothing variable. The modified cross-validation algorithm is able to tackle the computational burden caused by the model complexity, providing an important tool in semiparametric volatility estimation. We briefly discuss model identifiability when estimating volatility as well as nonnegativity of the resulting estimators. Furthermore, Monte Carlo simulations for several underlying generating models are implemented and applications to real data are provided.     

Optimal hedging through limit orders

This article applies the methods of stochastic dynamic programming to a risk management problem, where an agent hedges her derivative position by submitting limit orders. Therefore, this model is the first, in the literature on optimal trading with limit orders, to handle a problem of hedging options or other derivatives. A hedging strategy is developed where both the size and the limit price of each order is optimally set.     

Flood Catastrophe Model for Designing Optimal Flood Insurance Program: Estimating Location‐Specific Premiums in the Netherlands

As flood risks grow worldwide, a well‐designed insurance program engaging various stakeholders becomes a vital instrument in flood risk management. The main challenge concerns the applicability of standard approaches for calculating insurance premiums of rare catastrophic losses. This article focuses on the design of a flood‐loss‐sharing program involving private insurance based on location‐specific exposures. The analysis is guided by a developed integrated catastrophe risk management (ICRM) model consisting of a GIS‐based flood model and a stochastic optimization procedure with respect to location‐specific risk exposures. To achieve the stability and robustness of the program towards floods with various recurrences, the ICRM uses stochastic optimization procedure, which relies on quantile‐related risk functions of a systemic insolvency involving overpayments and underpayments of the stakeholders. Two alternative ways of calculating insurance premiums are compared: the robust derived with the ICRM and the traditional average annual loss approach. The applicability of the proposed model is illustrated in a case study of a Rotterdam area outside the main flood protection system in the Netherlands. Our numerical experiments demonstrate essential advantages of the robust premiums, namely, that they: (1) guarantee the program's solvency under all relevant flood scenarios rather than one average event; (2) establish a tradeoff between the security of the program and the welfare of locations; and (3) decrease the need for other risk transfer and risk reduction measures.     

Bayesian analysis of multivariate stochastic volatility with skew return distribution

Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew t-distributions are embedded to multivariate analysis with time-varying correlations. Bayesian modeling allows this approach to provide parsimonious skew structure and to easily scale up for high-dimensional problem. Analyses of daily stock returns are illustrated. Empirical results show that the time-varying correlations and the sparse skew structure contribute to improved prediction performance and Value-at-Risk forecasts.     

BL-GARCH models with elliptical distributed innovations

In this work, we discuss the class of bilinear GARCH (BL-GARCH) models that are capable of capturing simultaneously two key properties of non-linear time series: volatility clustering and leverage effects. It has often been observed that the marginal distributions of such time series have heavy tails; thus we examine the BL-GARCH model in a general setting under some non-normal distributions. We investigate some probabilistic properties of this model and we conduct a Monte Carlo experiment to evaluate the small-sample performance of the maximum likelihood estimation (MLE) methodology for various models. Finally, within-sample estimation properties were studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects. The main results suggest that the Student-t BL-GARCH seems highly appropriate to describe the S&P 500 daily returns.