A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function

In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the simple-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods for real data.Comment: 38 pages, 9 figures, 3 tables, changes: VAR(1)-CCC-GARCH(1,1) process dynamics and the analysis of increasing horizon are included in the simulation study, under revision in Annals of Operations Researc

Bayesian estimation of genetic parameters for multivariate threshold and continuous phenotypes and molecular genetic data in simulated horse populations using Gibbs sampling

<p>Abstract</p> <p>Background</p> <p>Requirements for successful implementation of multivariate animal threshold models including phenotypic and genotypic information are not known yet. Here simulated horse data were used to investigate the properties of multivariate estimators of genetic parameters for categorical, continuous and molecular genetic data in the context of important radiological health traits using mixed linear-threshold animal models via Gibbs sampling. The simulated pedigree comprised 7 generations and 40000 animals per generation. Additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits were simulated, resembling situations encountered in the Warmblood horse. Quantitative trait locus (QTL) effects and genetic marker information were simulated for one of the liabilities. Different scenarios with respect to recombination rate between genetic markers and QTL and polymorphism information content of genetic markers were studied. For each scenario ten replicates were sampled from the simulated population, and within each replicate six different datasets differing in number and distribution of animals with trait records and availability of genetic marker information were generated. (Co)Variance components were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. Residual variances were fixed to zero and a proper prior was used for the genetic covariance matrix.</p> <p>Results</p> <p>Effective sample sizes (ESS) and biases of genetic parameters differed significantly between datasets. Bias of heritability estimates was -6% to +6% for the continuous trait, -6% to +10% for the binary traits of moderate heritability, and -21% to +25% for the binary traits of low heritability. Additive genetic correlations were mostly underestimated between the continuous trait and binary traits of low heritability, under- or overestimated between the continuous trait and binary traits of moderate heritability, and overestimated between two binary traits. Use of trait information on two subsequent generations of animals increased ESS and reduced bias of parameter estimates more than mere increase of the number of informative animals from one generation. Consideration of genotype information as a fixed effect in the model resulted in overestimation of polygenic heritability of the QTL trait, but increased accuracy of estimated additive genetic correlations of the QTL trait.</p> <p>Conclusion</p> <p>Combined use of phenotype and genotype information on parents and offspring will help to identify agonistic and antagonistic genetic correlations between traits of interests, facilitating design of effective multiple trait selection schemes.</p

Unravelling the effects of age, period and cohort on metabolic syndrome components in a Taiwanese population using partial least squares regression

<p>Abstract</p> <p>Background</p> <p>We investigate whether the changing environment caused by rapid economic growth yielded differential effects for successive Taiwanese generations on 8 components of metabolic syndrome (MetS): body mass index (BMI), systolic blood pressure (SBP), diastolic blood pressure (DBP), fasting plasma glucose (FPG), triglycerides (TG), high-density lipoprotein (HDL), Low-density lipoproteins (LDL) and uric acid (UA).</p> <p>Methods</p> <p>To assess the impact of age, birth year and year of examination on MetS components, we used partial least squares regression to analyze data collected by Mei-Jaw clinics in Taiwan in years 1996 and 2006. Confounders, such as the number of years in formal education, alcohol intake, smoking history status, and betel-nut chewing were adjusted for.</p> <p>Results</p> <p>As the age of individuals increased, the values of components generally increased except for UA. Men born after 1970 had lower FPG, lower BMI, lower DBP, lower TG, Lower LDL and greater HDL; women born after 1970 had lower BMI, lower DBP, lower TG, Lower LDL and greater HDL and UA. There is a similar pattern between the trend in levels of metabolic syndrome components against birth year of birth and economic growth in Taiwan.</p> <p>Conclusions</p> <p>We found cohort effects in some MetS components, suggesting associations between the changing environment and health outcomes in later life. This ecological association is worthy of further investigation.</p

A New Approach to Age-Period-Cohort Analysis Using Partial Least Squares Regression: The Trend in Blood Pressure in the Glasgow Alumni Cohort

Due to a problem of identification, how to estimate the distinct effects of age, time period and cohort has been a controversial issue in the analysis of trends in health outcomes in epidemiology. In this study, we propose a novel approach, partial least squares (PLS) analysis, to separate the effects of age, period, and cohort. Our example for illustration is taken from the Glasgow Alumni cohort. A total of 15,322 students (11,755 men and 3,567 women) received medical screening at the Glasgow University between 1948 and 1968. The aim is to investigate the secular trends in blood pressure over 1925 and 1950 while taking into account the year of examination and age at examination. We excluded students born before 1925 or aged over 25 years at examination and those with missing values in confounders from the analyses, resulting in 12,546 and 12,516 students for analysis of systolic and diastolic blood pressure, respectively. PLS analysis shows that both systolic and diastolic blood pressure increased with students' age, and students born later had on average lower blood pressure (SBP: −0.17 mmHg/per year [95% confidence intervals: −0.19 to −0.15] for men and −0.25 [−0.28 to −0.22] for women; DBP: −0.14 [−0.15 to −0.13] for men; −0.09 [−0.11 to −0.07] for women). PLS also shows a decreasing trend in blood pressure over the examination period. As identification is not a problem for PLS, it provides a flexible modelling strategy for age-period-cohort analysis. More emphasis is then required to clarify the substantive and conceptual issues surrounding the definitions and interpretations of age, period and cohort effects

Re-interpreting conventional interval estimates taking into account bias and extra-variation

BACKGROUND: The study design with the smallest bias for causal inference is a perfect randomized clinical trial. Since this design is often not feasible in epidemiologic studies, an important challenge is to model bias properly and take random and systematic variation properly into account. A value for a target parameter might be said to be "incompatible" with the data (under the model used) if the parameter's confidence interval excludes it. However, this "incompatibility" may be due to bias and/or extra-variation. DISCUSSION: We propose the following way of re-interpreting conventional results. Given a specified focal value for a target parameter (typically the null value, but possibly a non-null value like that representing a twofold risk), the difference between the focal value and the nearest boundary of the confidence interval for the parameter is calculated. This represents the maximum correction of the interval boundary, for bias and extra-variation, that would still leave the focal value outside the interval, so that the focal value remained "incompatible" with the data. We describe a short example application concerning a meta analysis of air versus pure oxygen resuscitation treatment in newborn infants. Some general guidelines are provided for how to assess the probability that the appropriate correction for a particular study would be greater than this maximum (e.g. using knowledge of the general effects of bias and extra-variation from published bias-adjusted results). SUMMARY: Although this approach does not yet provide a method, because the latter probability can not be objectively assessed, this paper aims to stimulate the re-interpretation of conventional confidence intervals, and more and better studies of the effects of different biases

The Interplay of Variants Near LEKR and CCNL1 and Social Stress in Relation to Birth Size

Background We previously identified via a genome wide association study variants near LEKR and CCNL1 and in the ADCY5 genes lead to lower birthweight. Here, we study the impact of these variants and social stress during pregnancy, defined as social adversity and neighborhood disparity, on infant birth size. We aimed to determine whether the addition of genetic variance magnified the observed associations. Methodology/Principal Findings We analyzed data from the Northern Finland Birth Cohort 1986 (n = 5369). Social adversity was defined by young maternal age (<20 years), low maternal education (<11 years), and/or single marital status. Neighborhood social disparity was assessed by discrepancy between neighborhoods relative to personal socio-economic status. These variables are indicative of social and socioeconomic stress, but also of biological risk. The adjusted multiple regression analysis showed smaller birth size in both infants of mothers who experienced social adversity (birthweight by −40.4 g, 95%CI −61.4, −19.5; birth length −0.14 cm, 95%CI −0.23, −0.05; head circumference −0.09 cm 95%CI −0.15, −0.02) and neighborhood disparity (birthweight −28.8 g, 95%CI −47.7, −10.0; birth length −0.12 cm, 95%CI −0.20, −0.05). The birthweight-lowering risk allele (SNP rs900400 near LEKR and CCNL1) magnified this association in an additive manner. However, likely due to sample size restriction, this association was not significant for the SNP rs9883204 in ADCY5. Birth size difference due to social stress was greater in the presence of birthweight-lowering alleles. Conclusions/Significance Social adversity, neighborhood disparity, and genetic variants have independent associations with infant birth size in the mutually adjusted analyses. If the newborn carried a risk allele rs900400 near LEKR/CCNL1, the impact of stress on birth size was stronger. These observations give support to the hypothesis that individuals with genetic or other biological risk are more vulnerable to environmental influences. Our study indicates the need for further research to understand the mechanisms by which genes impact individual vulnerability to environmental insults

Hierarchical Models in the Brain

This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain