Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix

This paper studies the optimal portfolio selection problem in jump-diffusion models where an investor has a HARA utility function, and there are potentially a large number of assets and state variables. More specifically, we incorporate jumps into both stock returns and state variables, and then derive semi-analytical solutions for the optimal portfolio policy up to solving a set of ordinary differential equations to greatly facilitate economic insights and empirical applications of jump-diffusion models. To examine the effect of jump risk on investors’ behavior, we apply our results to the bond-stock mix problem and particularly revisit the bond/stock ratio puzzle in jump-diffusion models. Our results cast new light on this puzzle that unlike pure-diffusion models, it cannot be rationalized by the hedging demand assumption due to the presence of jumps in stock returns

Solitary waves and their stability in colloidal media: semi-analytical solutions

Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas compressibility. Semi-analytical solutions, for both one and two spatial dimensions, are derived using an averaged Lagrangian and suitable trial functions for the solitary waves. Power versus propagation constant curves and neutral stability curves are obtained for both cases, which illustrate that multiple solution branches occur for both the one and two dimensional geometries. For the one-dimensional case it is found that three solution branches (with a bistable regime) occur, while for the two-dimensional case two solution branches (with a single stable branch) occur in the limit of low background packing fractions. For high background packing fractions the power versus propagation constant curves are monotonic and the solitary waves stable for all parameter values. Comparisons are made between the semi-analytical and numerical solutions, with excellent comparison obtained.Comment: Paper to appear in Dynamics of Continuous, Discrete and Impulsive Systems, Series

Semi-analytical homologous solutions of the gravo-magnetic contraction

We propose an extension of the semi-analytical solutions derived by Lin et al. (1965) describing the two-dimensional homologous collapse of a self-gravitating rotating cloud having uniform density and spheroidal shape, which includes magnetic field (with important restrictions) and thermal pressure. The evolution of the cloud is reduced to three time dependent ordinary equations allowing to conduct a quick and preliminary investigation of the cloud dynamics during the precollapse phase, for a wide range of parameters. We apply our model to the collapse of a rotating and magnetized oblate and prolate isothermal core. Hydrodynamical numerical simulations are performed and comparison with the semi-analytical solutions is discussed. Under the assumption that all cores are similar, an apparent cloud axis ratio distribution is calculated from the sequence of successive evolutionary states for each of a large set of initial conditions. The comparison with the observational distribution of the starless dense cores belonging to the catalog of Jijina et al. (1999) shows a good agreement for the rotating and initially prolate cores (aspect ratio $\simeq 0.5$) permeated by an helical magnetic field ($\simeq 17-20 \mu$G for a density of $\simeq 10^4$ cm$^{-3}$).Comment: accepted for publication in A&

Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri

This study explores the semi-analytical solutions of the third-order dispersive equation with reaction (Fisher-like) term. Recently,the proposed problem has been exactly solved in the literature. Additionally, the semi-analytical solutions are needed to understandthe sensitivity of homotopy based methods in solving the proposed reaction-dispersion equation. Using symbolic computation withcarefully chosen perturbation parameters, the semi-analytical solutions are compared with the exact solutions, in order to show theefficiency of homotopy and Padé techniques. Obtained solutions, which can play key role in modelling reaction in a dispersive medium,are illustrated and discussed.Bu çalışma, üçüncü mertebeden reaksiyon terimli dağılım(dispersive) denkleminin yarı analitik çözümlerini üzerinedir. Son zamanlarda ele alınan problem literatürde tam olarak çözülmüştür. Ayrıca, yarı analitik çözümler, önerilen reaksiyon-dağılım denkleminin çözümünde homotopi temelli yöntemlerin hassasiyetini anlamak için gereklidir. Seçilen pertürbasyon parametreleri ile sembolik hesaplama kullanarak, yarı analitik çözümler, homotopi ve Padé tekniklerinin verimliliğini göstermek için kesin çözümlerle karşılaştırılmaktadır. Elde edilen çözümler dağılımlı ortamda reaksiyon modellemesinde büyük rol oynamaktadır

Cubic autocatalysis in a reaction-diffusion annulus: semi-analytical solutions

Semi-analytical solutions for cubic autocatalytic reactions are considered in a circularly symmetric reaction-diffusion annulus. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for this novel geometry. Singularity theory is used to determine the regions of parameter space in which the different types of steady-state diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found using a degenerate Hopf bifurcation analysis. A novel feature of this geometry is the effect, of varying the width of the annulus, on the static and dynamic multiplicity. The results show that for a thicker annulus, Hopf bifurcations and multiple steady-state solutions occur in a larger portion of parameter space. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with numerical solutions of the governing partial differential equations

Localization analysis of variationally based gradient plasticity model

The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient plasticity with linear softening is used, and the ensuing jump conditions and boundary conditions are discussed. Three cases with different regularity of the stress distribution are considered, and the problem is converted to a dimensionless form. Relations linking the load level, size of the plastic zone, distribution of plastic strain and plastic elongation of the bar are derived and compared to another, previously analyzed gradient formulation.Comment: 42 pages, 11 figure