Weak KAM Approach to First-Order Mean Field Games with State Constraints

We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon T goes to infinity. For this purpose, we analyze first Hamilton–Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on [0, T] converges to the solution of the ergodic system as T goes to infinity.

A Benchmarked Evaluation of a Selected CapitalCube Interval-Scaled Market Performance Variable

Context In this fifth analysis of the CapitalCube™ Market Navigation Platform[CCMNP], the focus is on the CaptialCube Closing Price Latest [CCPL] which, is an Interval Scaled Market Performance [ISMP] variable that seems, a priori, the key CCMNP information for tracking the price of stocks traded on the S&P500. This study follows on the analysis of the CCMNP’s Linguistic Category MPVs [LCMPV] where it was reported that the LCMPV were not effective in signaling impending Turning Points [TP] in stock prices. Study Focus As the TP of an individual stock is the critical point in the Panel and was used previously in the evaluation of the CCMNP, this study adopts the TP as the focal point in the evaluation montage used to determine the market navigation utility of the CCPL. This study will use the S&P500 Panel in an OLS Time Series [TS] two-parameter linear regression context: Y[S&P500] = X[TimeIndex] as the Benchmark for the performance evaluation of the CCPL in the comparable OLS Regression: Y[S&P500] = X[CCPL]. In this regard, the inferential context for this comparison will be the Relative Absolute Error [RAE] using the Ergodic Mean Projection [termed the Random Walk[RW]] of the matched-stock price forecasts three periods after the TP. Results Using the difference in the central tendency of the RAEs as the effect-measure, the TS: S&P Panel did not test to be different from the CCPL-arm of the study; further neither outperformed the RW; all three had Mean and Median RAEs that were greater than 1.0—the standard cut-point for rationalizing the use of a particular forecasting model. Additionally, an exploratory analysis used these REA datasets blocked on: (i) horizons and (ii) TPs of DownTurns & UpTurns; this analysis identified interesting possibilities for further analyses.

Meningkatkan Ketahanan Wilayah Melalui Estimasi Underreported Data Kejahatan Menggunakan Pendekatan Bayes

ABSTRACTThis paper present a study for the number of crime that run into underreporting counts. The purpose of the analysis is to estimate parameter of the model which is the actual number of crime. The model is a mixture of the poisson and the binomial distributions developed by Winkelmann (1996). The parameters of the model are estimated by Bayesian approach and Markov Chain Monte Carlo simulation using Gibbs sampling algorithm. Determination the convergence of the algorithm using trace plot, autocorrelation plot and ergodic mean plot. In the end, estimator of the parameters of the underreported counts model are the simulation sample mean that calculated from the simulation sample of iteration after burn in period until the last iteration.ABSTRAKPenelitian ini mengkaji permodelan data tingkat kejahatan yang mengalami underreporting counts. Tujuan analisis ini adalah untuk menaksir parameter model yaitu banyaknya jumlah tindak kejahatan yang sebenarnya. Model yang digunakan adalah hasil penggabungan antara distribusi poisson dan distribusi binomial yang dikembengkan oleh Winkelmann (1996). Penaksiran parameter model dilakukan melalui pendekatan bayes dan simulasi Markov Chain Monte Carlo menggunakan algoritma gibbs sampling. Penentuan konvergensi algoritma akan dilakukan melalui trace plot, autocorrelation plot, dan ergodic mean plot. Taksiran parameter model diperoleh dari rata-rata nilai sampel hasil simulasi yang dihitung dari iterasi setelah burn in period sampai dengan iterasi yang terakhir.