Two sided analysis of variance with a latent time series

Many real life regression problems exhibit some kind of calender time dependency and it is often of interest to predict the behavior of the regression function along this calender time direction. This can be formulated as a regression model with an added latent time series and the task is to be able to analyse this series. In this paper we engage this through a two step procedure, firstly we treat the time dependent elements as parameters and estimate them in the two-sided analysis of variance setup, secondly we use the estimated time series as predictor of the latent time series. An application to risk theory is discussed.regression, time series, risk theory

Nonparametric Regression with a Latent Time Series

In this paper we investigate a class of semiparametric models for panel datasetswhere the cross-section and time dimensions are large. Our model contains alatent time series that is to be estimated and perhaps forecasted along with anonparametric covariate effect. Our model is motivated by the need to be flexiblewith regard to functional form of covariate effects but also the need to be practicalwith regard to forecasting of time series effects. We propose estimation proceduresbased on local linear kernel smoothing; our estimators are all explicitly given. Weestablish the pointwise consistency and asymptotic normality of our estimators. Wealso show that the effects of estimating the latent time series can be ignored incertain cases.Kernel Estimation, Forecasting, Panel Data, Unit Roots

Kernel Density Estimation of Actuarial Loss Functions.

No abstractLoss models; Transformation; Skewness; Weighted integrated squared error

Asymmetric information, self-selection and pricing of insurance contracts: the simple no-claims case

This paper presents an optional bonus-malus contract based on a pri-ori risk classification of the underlying insurance contract. By inducing self-selection, the purchase of the bonus-malus contract can be used as a screening device. This gives an even better pricing performance than both an experience rating scheme and a classical no-claims bonus system. An application to the Danish automobile insurance market is considered

Yield Curve Estimation by Kernel Smoothing Methods

We introduce a new method for the estimation of discount functions, yield curves and forward curves from government issued coupon bonds. Our approach is nonparametric and does not assume a particular functional form for the discount function although we do show how to impose various restrictions in the estimation. Our method is based on kernel smoothing and is defined as the minimum of some localized population moment condition. The solution to the sample problem is not explicit and our estimation procedure is iterative, rather like the backfitting method of estimating additive nonparametric models. We establish the asymptotic normality of our methods using the asymptotic representation of our estimator as an infinite series with declining coefficients. The rate of convergence is standard for one dimensional nonparametric regression. We investigate the finite sample performance of our method, in comparison with other well-established methods, in a small simulation experiment.Coupon bonds, kernel estimation, Hilbert space, nonparametric regression, term structure estimation, yield curve, zero coupon.

Estimating Multiplicative and Additive Hazard Functions by Kernel Methods

We propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models. We work with a full counting process framework that allows for left truncation and right censoring. Our procedures are based on kernels and on the idea of marginal integration. We provide a central limit theorem for our estimator.Additive model, censoring, kernel, proportional hazards, survival analysis

Fundamentals of Cost and Risk that Matter to Pension Savers and Life Annuitants

This chapter analyzes two types of investment strategies for an investor with a savings plan for retirement. In one, the investor sets an upper target which his wealth should not go above. In the other, the investor adds a lower target which his wealth should not go below. The analysis is done in a Black-Scholes model with one risky stock and one risk-free bond, with the restriction that the investor cannot invest more than his current wealth in the risky stock. We illustrate the results by describing a 30-year horizon. We use quantiles of the terminal wealth distribution or the level of accumulated wealth obtained by a given percentage of investors who follow the recommended strategy. The embedded guarantee and freedom to choose the upper and lower bounds represent the main appeal of this approach. We discuss the connection between expected return, affordable risk, and transparent fees for funds management