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

Truncating SRCAP variants outside the Floating-Harbor syndrome locus cause a distinct neurodevelopmental disorder with a specific DNA methylation signature

Truncating variants in exons 33 and 34 of the SNF2-related CREBBP activator protein (SRCAP) gene cause the neurodevelopmental disorder (NDD) Floating-Harbor syndrome (FLHS), characterized by short stature, speech delay, and facial dysmorphism. Here, we present a cohort of 33 individuals with clinical features distinct from FLHS and truncating (mostly de novo) SRCAP variants either proximal (n = 28) or distal (n = 5) to the FLHS locus. Detailed clinical characterization of the proximal SRCAP individuals identified shared characteristics: developmental delay with or without intellectual disability, behavioral and psychiatric problems, non-specific facial features, musculoskeletal issues, and hypotonia. Because FLHS is known to be associated with a unique set of DNA methylation (DNAm) changes in blood, a DNAm signature, we investigated whether there was a distinct signature associated with our affected individuals. A machine-learning model, based on the FLHS DNAm signature, negatively classified all our tested subjects. Comparing proximal variants with typically developing controls, we identified a DNAm signature distinct from the FLHS signature. Based on the DNAm and clinical data, we refer to the condition as "non-FLHS SRCAP-related NDD.'' All five distal variants classified negatively using the FLHS DNAm model while two classified positively using the proximal model. This suggests divergent pathogenicity of these variants, though clinically the distal group presented with NDD, similar to the proximal SRCAP group. In summary, for SRCAP, there is a clear relationship between variant location, DNAm profile, and clinical phenotype. These results highlight the power of combined epigenetic, molecular, and clinical studies to identify and characterize genotype-epigenotype-phenotype correlations