Abstract
We introduce an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities driven by multi-dimensional Brownian motion. We then provide a detailed analysis of the optimal consumption, investment and insurance purchase strategies for the wage earner whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming methods to obtain explicit solutions for the case of discounted constant relative risk aversion utility functions and describe new analytical results which are presented together with the corresponding economic interpretations.

Abstract
Let f and g be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy h between f and g is C-1 at a point in the nearby expanding set of f, then h is a smooth diffeomorphism in the basin of attraction of a renormalization interval of f. In particular, if f:I -> I and g : J -> J are C-r unimodal maps and h is C-1 at a boundary of I, then h is C-r in I.

Abstract

Abstract
We consider two sampling plans by variables to inspect batches of products from an industrial process under a context of unknown distribution underlying the measurements of the quality characteristic under study. Through the use of the bootstrap methodology and Monte Carlo simulations we evaluate and compare the performance of those sampling plans in terms of probability of acceptance of lots and average outgoing quality level.

Abstract
In real situations the evaluation of the global quality of either a product or a service depends on more than one quality characteristic. In order to monitor the variability of multivariate processes and identify the variables responsible for changes in the process, we will use the STATIS (Structuration des Tableaux A Trois Indices de la Statistique) methodology, a three-way data analysis method. For this purpose we consider a control chart based on a similarity measure between two positive semi-definite matrices, the RV coefficient, and we evaluate the performance of this control chart for monitoring multivariate normal data.

Abstract
A control chart based on the quantile function to monitor the shape parameter of a Weibull distribution is proposed and its performance is analyzed by Monte Carlo simulation. The importance of monitoring the shape parameter even when the other parameters of the Weibull distribution are assumed known is further enhanced, together with motivating examples. © 2014 Proceedings of COMPSTAT 2014 - 21st International Conference on Computational Statistics. All rights reserved.