Efficient Stochastic Tail Modeling with Small Sample ... - U.I.U.C. Math
Recommend Documents
Oct 16, 2014 - butions through nonlinear system dynamics; second, chance constrained optimization problems are in general com- putationally intractable ...
Nov 29, 2018 - local minimum within ËO(n + n2/3/ϵ3/2)1 Hessian sample .... Notation: We use a(x) = O(b(x)) if a(x) ⤠Cb(x), where C is a constant .... Under Assumptions 3.1 and 3.2, suppose that n > 10,Ms,t > 2L2 and Dh > 25 log d. Let αs,t ...
Abstract. Despite the widespread use of upâdown staircases in adaptive threshold estimation, their efficiency and usability in forced-choice experiments has ...
Despite the widespread use of upâdown staircases in adaptive threshold estimation, their efficiency and usability in forced-choice experiments has been ...
Feb 17, 2011 - main mathematical abstractions which have been employed to address ... problem of cooperative solution to distributed optimization problems [6]â[11]. ... to agree are free to lie in the Euclidean space. ...... 988â1001, 2003. ....
Jul 20, 2005 - The modeling of probability density distributions of coefficients produced by the discrete cosine .... An alternative approach is to consider the log-likelihood (LL) function under ..... Using the Cauchy-Schwarz inequality,. ( L. â.
Mar 4, 2014 - OpenLabFramework is a newly developed web-application for ... With the development of high-throughput technologies, laboratory ... issue, especially since most laboratories still attempt to keep track of their samples using spreadsheet
Nov 1, 2001 - The reaction term is assumed to have polynomial .... bounded linear operators T : X â Y, endowed with the sup-norm. When X = Y we write ...
What is AJAX? AJAX is a technology used to facilitate real-time data changes
and updates on a page without requiring a page reload. AJAX stands for ...
May 7, 2012 - daily basis [15]. ... learning parameter update proceeds as long as local agreement on average gradient are reached; .... Denote wk(t) as the weight vector available on node k at time t, and gk(t) the gradient evaluated. 4 ...
... by some states. Alternate Common Core activities are included in the Daily
Lesson Plan ... Subtracting three-digit numbers, regrouping only with tens and no
zero in the tens. 42 .... a Third Grade Projectable Lesson CD (see page i16), it will
26 Oct 2007 ... Blair & IB Entrance Exam Math Prep Issue 6. – 1 –. This packet is designed for
SAMPLE ONLY only. No copying is allowed. Report any illegal ...
Accuplacer Sample Questions. Page 1 of 7. Accuplacer Sample Questions. Math
Only. There is one general math test for RCC no matter what your acdemic ...
black. Box B contains 7 marbles, of which two are white and five are black. You have to .... We have tested a game of dice in 4 first grade classes in Stuttgart and ...
1ббб UIUC Undergraduate Math Contest. Solutions. Problem 1. Let an denote
the integer closest to /Й. (For example, ai = a2 = 1 and a3 = a4 = 2 since. /1 = 1, /2
...
threshold, thus the name tail-equivalent linearization. Once the TELS is defined for a specific response threshold, methods of linear random vibration analysis ...
joint STTR project with Genoa Software Systems, Inc., for the Army Research Of- fice; and by the Virginia Center for Innovative Technology under grant ...
Petri nets such as stochastic reward nets, or continuous time Markov chains, e.g., ... service from something unspecified (Pioro and Medhi 2004, Guo 2007), .... of the network resources that brings the system back to fault free operation. .... of a f
Oct 1, 2018 - particle-based stochastic simulations of biochemical systems in complex three ..... The Display Options control the molecule's shape, size, color, and brightness ...... 'On explosions of solutions to a system of partial differential.
AbstractâThis paper proposes a novel multifractal traffic model, and an associated parameter fitting procedure, based on stochastic L-Systems, which were ...
Feb 10, 2015 - of the covariance matrix of the outcome variable. ... for binary outcomes and approximately 50 clustering units for continuous outcomes ( ..... However, MLM fixed ..... Intraclass correlation values for planning group-randomized.
Small-Sample Equating With Prior Information. Samuel A. Livingston and Charles Lewis. ETS, Princeton, New Jersey. June 2009 ...
ABSTRACT. One of the challenges of stochastic asset/liability modeling for large insurance businesses is the run time. Using a complete stochastic asset/liability ...
ЫÐ(g âЫ УТШ 729#@ EP5âXâ ` ¢wb"ScÐ0. (16). Evaluating Eq. (16) at time iE{( and taking into ac- count Eq. (14), the coefficients âЫ may be obtained as.
Efficient Stochastic Tail Modeling with Small Sample ... - U.I.U.C. Math
Stand alone desktop software suite communicating to Microsoft. Excel and ... Consolidated Insurance Business: Interest Rate Sampling. Algorithms.
Efficient Stochastic Tail Modeling with Small Sample Runs: Tackling Sampling Errors and Sampling Bias by Pivot-Distance Sampling and Parametric Curve Fitting Techniques and Tools Yvonne C. Chueh, PhD, ASA Paul H. Johnson, Jr., PhD
Joint work between the University of Illinois at Urbana-Champaign (UIUC) and Central Washington University (CWU) Funded by The Actuarial Foundation
Y. C. Chueh and P. H. Johnson Jr ()
August 2012
1 / 15
Introduction and Purpose
Introduction Practitioners/researchers are challenged to make credible inferential statements about population distributions of critical variables Well known challenge of running a stochastic asset/liability model is the long run-time - using small risk scenario samples can introduce sampling errors Well known challenge of fitting a distribution to economic data is sampling bias arising from small risk scenario samples Successful projection of the universe of critical financial outcomes for a large population of policyholders is important Pricing, reserving, budgeting risk capital
Y. C. Chueh and P. H. Johnson Jr ()
August 2012
2 / 15
Introduction and Purpose
Purpose
We discuss the development of two open source, high performance computation software tools that reduce sampling errors and bias arising from small risk scenario samples to replicate a large population distribution, especially at the tails CSTEP (reducing sampling errors): http://www.cwu.edu/ chueh/ AMOOF2 (fitting distributions and reducing sampling bias): http://amoof.amp-software.net/index.php
Y. C. Chueh and P. H. Johnson Jr ()
August 2012
3 / 15
CSTEP
CSTEP Introduction
CSTEP: Cluster Sampling for Tail Estimation of Probability Distribution of Financial Model Outcome Upgrade from spreadsheet-based SALMS (Stochastic Asset Liability Model Sampling) used since 2003 CSTEP is open source, high performance computation software Universe capacity: 8,388,608 scenarios with up to 4500 time periods each Flexible sample size, reversible and reusable sampling Rate sampling (interest rate, equity return, index)
Y. C. Chueh and P. H. Johnson Jr ()
August 2012
4 / 15
CSTEP
CSTEP Algorithms: Representative Scenarios Consider a population of N rate paths Editable distance formulas similar to Euclidean distance are used to select n representative (pivot) scenarios where n
