We study a family of optimal control problems in which one aims at minimizing cost that mixes quadratic penalization and the variance system, both for finitely many agents mean-field dynamics as their number goes to infinity. While solutions discrete problem always exist unique explicit form, behavior macroscopic counterparts is very sensitive magnitude time horizon parameter. When minimizes fi...

Portfolio Optimization is based on the efficient allocation of several assets, which can get heavily affected by uncertainty in input parameters. So we must look for such solutions give us steady results uncertain conditions too. Recently, optimization problems are being dealt with robust approach. With this development, interest researchers has been shifted toward portfolio optimization. In pa...

We consider the problem of estimating a measure of daily volatility from intermittent high-frequency data that are subject to market microstructure effects. We show that a simple Newey-West type modification of the realized variance (RV) yields an unbiased measure of volatility for the ‘open’ part of the day. The modified RV is unbiased even if 1-minute intra-day returns are used. Further, with...

In a linear regression model with homoscedastic Normal noise, I consider James–Stein type shrinkage in the estimation of nuisance parameters associated with control variables. For at least three control variables and exogenous treatment, I show that the standard leastsquares estimator is dominated with respect to squared-error loss in the treatment effect even among unbiased estimators and even...

Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to half the test duration. As a descriptive statistic, Total variance performs an exact decomposition of the sample variance of the frequency residuals into components associated with descending frequency octaves. As an estimator of Allan variance, Total variance has modest bias an...

In this paper, we apply the Markowitz portfolio optimization technique based on mean-variance and semi-variance as measures of risk stocks listed South Pacific Stock Exchange, Fiji. We document key market characteristics consider monthly returns data from SEP-2019 to FEB-2022 (T = 30) 17/19 companies stock exchange construct various portfolios like 1/N (naïve), maximum return, minimum-variance ...