scholarly journals Optimal learning with non-Gaussian rewards

2016 ◽  
Vol 48 (1) ◽  
pp. 112-136 ◽  
Author(s):  
Zi Ding ◽  
Ilya O. Ryzhov
Keyword(s):  
Free Boundary ◽  
Gittins Index ◽  
Index Policy ◽  
Infinitely Divisible ◽  
Optimal Learning ◽  
Optimal Stopping Theory ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Index Value

Abstract We propose a novel theoretical characterization of the optimal 'Gittins index' policy in multi-armed bandit problems with non-Gaussian, infinitely divisible reward distributions. We first construct a continuous-time, conditional Lévy process which probabilistically interpolates the sequence of discrete-time rewards. When the rewards are Gaussian, this approach enables an easy connection to the convenient time-change properties of a Brownian motion. Although no such device is available in general for the non-Gaussian case, we use optimal stopping theory to characterize the value of the optimal policy as the solution to a free-boundary partial integro-differential equation (PIDE). We provide the free-boundary PIDE in explicit form under the specific settings of exponential and Poisson rewards. We also prove continuity and monotonicity properties of the Gittins index in these two problems, and discuss how the PIDE can be solved numerically to find the optimal index value of a given belief state.

Learning for infinitely divisible GARCH models in option pricing

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Fumin Zhu ◽  
Michele Leonardo Bianchi ◽  
Young Shin Kim ◽  
Frank J. Fabozzi ◽  
Hengyu Wu
Keyword(s):  
Option Pricing ◽  
Stock Returns ◽  
Bayesian Learning ◽  
Space Structure ◽  
Estimation Methods ◽  
Garch Models ◽  
Learning Approaches ◽  
Infinitely Divisible ◽  
Asymmetric Garch ◽  
Non Gaussian

AbstractThis paper studies the option valuation problem of non-Gaussian and asymmetric GARCH models from a state-space structure perspective. Assuming innovations following an infinitely divisible distribution, we apply different estimation methods including filtering and learning approaches. We then investigate the performance in pricing S&P 500 index short-term options after obtaining a proper change of measure. We find that the sequential Bayesian learning approach (SBLA) significantly and robustly decreases the option pricing errors. Our theoretical and empirical findings also suggest that, when stock returns are non-Gaussian distributed, their innovations under the risk-neutral measure may present more non-normality, exhibit higher volatility, and have a stronger leverage effect than under the physical measure.

scholarly journals Development and Characterization of Biocompatible Membranes from Natural Chitosan and Gelatin for Pervaporative Separation of Water–Isopropanol Mixture

Polymers ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2868
Author(s):  
Akshay S. Kulkarni ◽  
Ashok M. Sajjan ◽  
T. M. Yunus Khan ◽  
Irfan Anjum Badruddin ◽  
Sarfaraz Kamangar ◽  
...  
Keyword(s):  
Surface Characteristics ◽  
Permeation Flux ◽  
X Ray Diffraction ◽  
Natural Polymers ◽  
X Ray ◽  
Efficient Separation ◽  
Differential Scanning Colorimetry ◽  
Index Value ◽  
Pervaporation Separation

Natural polymers have attracted a lot of interest in researchers of late as they are environmentally friendly, biocompatible, and possess excellent characters. Membranes forming natural polymers have provided a whole new dimension to the separation technology. In this work, chitosan-gelatin blend membranes were fabricated using chitosan as the base and varying the amount of gelatin. Transport, mechanical, and surface characteristics of the fabricated membranes were examined in detail by means of the characterizing techniques such as Fourier transform infrared spectroscopy, differential scanning colorimetry, wide angle X-ray diffraction, scanning electron microscope, and thermogravimetric analysis. In order to analyze the water affinity of the developed blend chitosan-gelatin membranes, the percentage degree of swelling was examined. Out of the fabricated membranes, the membrane loaded with 15 mass% of gelatin exhibited the better pervaporation performance with a pervaporation separation index value of 266 at 30 °C for the solution containing 10% in terms of the mass of water, which is the highest among the contemporary membranes. All the fabricated membranes were stable during the pervaporation experiments, and permeation flux of water for the fabricated membranes was dominant in the overall total permeation flux, signifying that the developed membranes could be chosen for efficient separation of water–isopropanol mixture on a larger scale.

scholarly journals Morphometric Characterization of Small Cell Lymphocytic Lymphoma

2014 ◽  
Vol 20 (4) ◽  
pp. 179-183
Author(s):  
Anca Chisoi ◽  
Mariana Aşchie ◽  
I. Poinăreanu
Keyword(s):  
Small Population ◽  
Small Cell ◽  
Nuclear Area ◽  
Cytoplasmic Area ◽  
Irregularity Index ◽  
Microscopic Features ◽  
Field Measuring ◽  
Index Value ◽  
Morphometric Characterization

Abstract The morphometry in histopathology is used to characterize cell populations belonging to different tissues and to identify differences in their parameters with prognostic implications. To achieve morphometric examination were selected 6 of 24 cases identified as small cell lymphocytic lymphoma. For each case analysis was done on five fields, for each field measuring the parameters of 20 cells. The studied parameters were for cytoplasm: cytoplasmic area, maximum and minimum cytoplasmic diameter, cytoplasmic perimeter; for nucleus were measured: nuclear area, minimum and maximum nuclear diameter, nuclear perimeter, nuclear contour index, nuclear ellipticity index, nuclear irregularity index. Also the nucleocytoplasmic ratio was calculated in all studied cases. Small cell lymphocytic lymphoma is characterized in morphometric terms having a small cytoplasmic area (average 29.206) and also a small nuclear area (mean 28.939) having a nucleo-cytoplasmic ratio appearance suggestive for adult lymphocyte. A nuclear contour index small value (3.946), ellipticity index value also small (3.521) and small nuclear irregularity index (3.965). Standard deviations, in any of the studied morphometric categories, is around or below 1 suggesting monomorphic cell appearance. These morphometric and microscopic features characterized mainly by a small population of adult lymphocytes, monomorphic, with rounded hipercromic nuclei, dense chromatin, support the framing into indolent lymphoma group in terms of clinical outcome.

WEAK CONVERGENCE OF NONLINEAR TRANSFORMATIONS OF INTEGRATED PROCESSES: THE MULTIVARIATE CASE

2009 ◽  
Vol 25 (5) ◽  
pp. 1180-1207 ◽  
Author(s):  
Norbert Christopeit
Keyword(s):  
Weak Convergence ◽  
Recent Work ◽  
Invariance Principle ◽  
Nonlinear Transformations ◽  
New Class ◽  
Triangular Arrays ◽  
Integrable Functions ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Integrated Processes

We consider weak convergence of sample averages of nonlinearly transformed stochastic triangular arrays satisfying a functional invariance principle. A fundamental paradigm for such processes is constituted by integrated processes. The results obtained are extensions of recent work in the literature to the multivariate and non-Gaussian case. As admissible nonlinear transformation, a new class of functionals (so-called locally p-integrable functions) is introduced that adapts the concept of locally integrable functions in Pötscher (2004, Econometric Theory 20, 1–22) to the multidimensional setting.

scholarly journals Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 22 ◽  
Author(s):  
Jordi Belda ◽  
Luis Vergara ◽  
Gonzalo Safont ◽  
Addisson Salazar
Keyword(s):  
Signal Processing ◽  
Partial Correlation ◽  
Correlation Coefficients ◽  
Real Data ◽  
Linear Estimation ◽  
Precision Matrix ◽  
Conditional Mean ◽  
Graph Signal Processing ◽  
Gaussian Case ◽  
Non Gaussian

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.

Linear dynamic errors-in-variables models

1986 ◽  
Vol 23 (A) ◽  
pp. 23-39 ◽  
Author(s):  
M. Deistler
Keyword(s):  
Dynamical Systems ◽  
Transfer Functions ◽  
Errors In Variables ◽  
Linear Dynamical Systems ◽  
Linear Dynamic ◽  
Dynamic Errors ◽  
Non Gaussian ◽  
Inputs And Outputs

Linear dynamical systems where both inputs and outputs are contaminated by errors are considered. A characterization of the sets of all observationally equivalent transfer functions is given, the role of the causality assumption is investigated and conditions for identifiability in the case of Gaussian as well as non-Gaussian observations are derived.

Sign in / Sign up

Export Citation Format

Share Document