On the Gains of Using High Frequency Data in Portfolio Selection

Can VAR Models Capture Regime Shifts in Asset Returns? A Long-Horizon Strategic Asset Allocation Perspective

This paper examines an optimal investment–consumption problem in a setting where the financial environment is influenced by both stochastic factors and delayed effects. The investor, endowed with Constant Relative Risk Aversion (CRRA) preferences, allocates wealth between a risk-free asset and a single risky asset. The short rate follows a Vasiˇček-type term structure model, while the risky asset price dynamics are driven by a delayed Heston specification whose variance process evolves according to a Cox–Ingersoll–Ross (CIR) diffusion. Delayed dependence in the wealth dynamics is incorporated through two auxiliary variables that summarize past wealth trajectories, enabling us to recast the naturally infinite-dimensional delay problem into a finite-dimensional Markovian framework. Using Bellman’s dynamic programming principle, we derive the associated Hamilton–Jacobi–Bellman (HJB) partial differential equation and demonstrate that it generalizes the classical Merton formulation to simultaneously accommodate delay, stochastic interest rates, stochastic volatility, and consumption. Under CRRA utility, we obtain closed-form expressions for the value function and the optimal feedback controls. Numerical illustrations highlight how delay and market parameters impact optimal portfolio allocation and consumption policies.

We study a finite-horizon optimal consumption and investment problem in a complete continuous-time market where consumption is restricted within fixed upper and lower bounds. Assuming constant relative risk aversion (CRRA) preferences, we employ the dual-martingale approach to reformulate the problem and derive closed-form integral representations for the dual value function and its derivatives. These results yield explicit feedback formulas for the optimal consumption, portfolio allocation, and wealth processes. We establish the duality theorem linking the primal and dual value functions and verify the regularity and convexity properties of the dual solution. Our results show that the upper and lower consumption bounds transform the linear Merton rule into a piecewise policy: consumption equals L when wealth is low, follows the unconstrained Merton ratio in the interior region, and is capped at H when wealth is high.

Risk preferences broadly affect many economic decisions when markets are incomplete. Common representations of risk preferences are constant absolute, relative, and partial relative risk aversion. Each of these preference classes has distinct impacts on choice. An econometric test for distinguishing the class of preferences is proposed and implemented for potato supply response in Idaho. The data reject constant absolute and partial relative risk aversion and are congruent with constant relative risk aversion.

In practice, stock investment is one of the most important decisions made by households. The primary goal of this paper is to explain family investment decisions under the assumptions of household member’s preferences and efficient risk sharing based on the collective household model. In particular, by examining the absolute (relative) risk aversion of the household welfare function, we demonstrate how household’s portfolio allocation in stocks changes with family wealth. We examine two types of preference heterogeneity between family members: parameter heterogeneity and functional form heterogeneity. This study offers an alternative explanation of household portfolio choice corresponding with the observation that wealthier households tend to hold greater share of their wealth in risky assets. Specifically, if two decision-makers have standard constant relative risk aversion preference with different relative risk aversions in a household, family’s relative risk aversion decreases as household wealth increases (decreasing relative risk aversion).

The problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies, is the main focus of this paper. Several works in the literature, which deal either with optimal trading under static risk constraints or with VaR{based dynamic risk constraints, are extended. The market model considered is continuous in time and incomplete, and the prices of nancial assets are modeled by It^o processes. The dynamic risk constraints, which are time and state dependent, are generated by a general class of risk measures. Optimal trading strategies are characterized by a quadratic BSDE. Within the class of time consistent distortion risk measures, a three{fund separation result is established. Numerical results emphasize the eects of imposing risk constraints on trading.

Operative Use of Eddy Covariance Measurements: Are High Frequency Data Indispensable?

Optimal retirement consumption with a stochastic force of mortality

PurposeThis paper examines the relationship between volatility, sentiment and returns in terms of levels and changes for both lower and higher data frequencies using quantile regression (QR) method.Design/methodology/approachIn the first step, the study applies the Granger causality test to understand the causal relationship between realized volatility, returns and sentiment as levels and changes. In the second step, the study employs a QR method to investigate whether investor sentiment and returns can predict realized volatility. This regression method gives robust results irrespective of distributional assumptions and to outliers in the dependent variable.FindingsEmpirical results show that the VIX volatility index is a better fear gauge of market-wide investors' sentiments and has a predictive power for future realized volatility in terms of levels and changes for both higher and lower data frequencies. This study provides evidence that the relationship between realized volatility, investor sentiment and returns, respectively, is not symmetric for all quantiles of QR, as opposed to OLS regression. Furthermore, this work supports the behavioral theory beyond leverage hypothesis in explaining the asymmetric relation between returns and volatility at higher and lower data frequencies.Originality/valueThis paper adds to the limited understanding of investor sentiment’s impact on volatility by proposing a QR model which provides a more complete picture of the relationship at all parts of the volatility distribution for both higher and lower data frequencies and in terms of levels and changes. To the author knowledge, this is the first paper to study the volatility responses to positive and negative sentiment changes for developed market and to use both lower and higher data frequencies as well as data in terms of levels and changes.

Empirical risk aversion functions-estimates and assessment of their reliability

Importance sampling in stochastic optimization: An application to intertemporal portfolio choice

Positive and Negative Externalities in Innovation, Trade, and Regional Economic Growth

This paper is aimed at assessing the impact of the degree of relative risk aversion on economic welfare for different levels of the interest rate and the exchange rate depreciation in a small open beconomy. To do this, a representative consumer-producer makes decisions on consumption, money balances, and leisure. In order to find a closed-form solution of the household’s economic welfare, it is assumed that individual’s preferences belong to the family of Constant Relative Risk Aversion (CRRA) utility functions. Several comparative statics graphical experiments about the effects of the degree of relative risk aversion on economic welfare for different levels of nominal variables are carried out. Finally, we find that, under the stated assumptions, household’s economic welfare seen as a function of the degree of relative risk aversion is responsive to different values of nominal variables.

OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model whzere his income is generated by returns on assets and these returns or instantaneous growth rates are stochastic. P. A. Samuelson has developed a similar model in discrete-time for more general probability distributions in a companion paper [8]. I derive the optimality equations for a multiasset problem when the rate of returns are generated by a Wiener Brownian-motion process. A particular case examined in detail is the two-asset model with constant relative riskaversion or iso-elastic marginal utility. An explicit solution is also found for the case of constant absolute risk-aversion. The general technique employed can be used to examine a wide class of intertemporal economic problems under uncertainty. In addition to the Samuelson paper [8], there is the multi-period analysis of Tobin [9]. Phelps [6] has a model used to determine the optimal consumption rule for a multi-period example where income is partly generated by an asset with an uncertain return. Mirrless [5] has developed a continuous-time optimal consumption model of the neoclassical type with technical progress a random variable.

The effects of electrical vestibular stimulation upon movement and perception suggest two evoked sensations: head roll and inter-aural linear acceleration. The head roll vector causes walking subjects to turn in a direction dependent on head pitch, requiring generation of torque around a vertical axis. Here the effect of vestibular stimulation upon vertical torque (T(z)) was investigated during quiet stance. With the head tilted forward, square-wave stimuli applied to the mastoid processes evoked a polarity-specific T(z) response accompanied by trunk yaw. Stochastic vestibular stimulation (SVS) was used to investigate the effect of head pitch with greater precision; the SVS–T(z) cross-correlation displayed a modulation pattern consistent with the head roll vector and this was also reflected by changes in coherence at 2–3 Hz. However, a separate response at 7–8 Hz was unaffected by head pitch. Head translation (rather than rotation) had no effect upon this high frequency response either, suggesting it is not caused by a sense of body rotation induced by an inter-aural acceleration vector offset from the body. Instead, high coherence between medio-lateral shear force and T(z) at the same frequency range suggests it is caused by mechanical coupling to evoked medio-lateral sway. Consistent with this explanation, the 7–8 Hz response was attenuated by 90 deg head roll or yaw, both of which uncouple the inter-aural axis from the medio-lateral sway axis. These results demonstrate two vertical torque responses to electrical vestibular stimulation in standing subjects. The high frequency response can be attributed to mechanical coupling to evoked medio-lateral sway. The low frequency response is consistent with a reaction to a sensation of head roll, and provides a novel method for investigating proprioceptive-vestibular interactions during stance.