STOCHASTIC CLAIMS RESERVING VIA A BAYESIAN SPLINE MODEL WITH RANDOM LOSS RATIO EFFECTS

2017 ◽  
Vol 48 (1) ◽  
pp. 55-88 ◽  
Author(s):  
Guangyuan Gao ◽  
Shengwang Meng
Keyword(s):  
Random Effect ◽  
The United States ◽  
Basis Functions ◽  
Smoothing Spline ◽  
Period Effect ◽  
Proposed Model ◽  
Spline Basis ◽  
Lower Triangle ◽  
Shrinkage Priors ◽  
Insurance Data

AbstractWe propose a Bayesian spline model which uses a natural cubicB-spline basis with knots placed at every development period to estimate the unpaid claims. Analogous to the smoothing parameter in a smoothing spline, shrinkage priors are assumed for the coefficients of basis functions. The accident period effect is modeled as a random effect, which facilitate the prediction in a new accident period. For model inference, we use Stan to implement the no-U-turn sampler, an automatically tuned Hamiltonian Monte Carlo. The proposed model is applied to the workers' compensation insurance data in the United States. The lower triangle data is used to validate the model.

An Empirical Bargaining Model with Left-Digit Bias: A Study on Auto Loan Monthly Payments

2021 ◽  
Author(s):  
Zhenling Jiang
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Large Data ◽  
The United States ◽  
Nash Bargaining ◽  
Bargaining Model ◽  
Data Set ◽  
Proposed Model ◽  
Lower Interest Rate ◽  
The Empirical Analysis

This paper studies price bargaining when both parties have left-digit bias when processing numbers. The empirical analysis focuses on the auto finance market in the United States, using a large data set of 35 million auto loans. Incorporating left-digit bias in bargaining is motivated by several intriguing observations. The scheduled monthly payments of auto loans bunch at both $9- and $0-ending digits, especially over $100 marks. In addition, $9-ending loans carry a higher interest rate, and $0-ending loans have a lower interest rate. We develop a Nash bargaining model that allows for left-digit bias from both consumers and finance managers of auto dealers. Results suggest that both parties are subject to this basic human bias: the perceived difference between $9- and the next $0-ending payments is larger than $1, especially between $99- and $00-ending payments. The proposed model can explain the phenomena of payments bunching and differential interest rates for loans with different ending digits. We use counterfactuals to show a nuanced impact of left-digit bias, which can both increase and decrease the payments. Overall, bias from both sides leads to a $33 increase in average payment per loan compared with a benchmark case with no bias. This paper was accepted by Matthew Shum, marketing.

scholarly journals Phenotypic Characteristics Associated with Shelter Dog Adoption in the United States

Animals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1959
Author(s):  
Cassie J. Cain ◽  
Kimberly A. Woodruff ◽  
David R. Smith
Keyword(s):  
Random Effect ◽  
Electronic Record ◽  
The United States ◽  
Simple Random Sample ◽  
Adult Size ◽  
Phenotypic Characteristics ◽  
Record Keeping ◽  
The North ◽  
Cox Proportional Hazard ◽  
Shelter Dog

The objective of this study was to identify phenotypic characteristics of dogs predictive of adoption after being received into a shelter. Individual dog records for 2017 were requested from shelters in five states that received municipal funding and utilized electronic record keeping methods. Records from 17 shelters were merged into a dataset of 19,514 potentially adoptable dogs. A simple random sample of 4500 dogs was used for modelling. Variables describing coat length, estimated adult size, and skull type were imputed from breed phenotype. A Cox proportional hazard model with a random effect of shelter was developed for the outcome of adoption using manual forward variable selection. Significance for model inclusion was set at alpha = 0.05. Dogs from shelters in the North were more likely to be adopted than dogs from shelters in the South (hazard ratio (HR) = 3.13, 95% C.I. 1.27–7.67), as were dogs from Western shelters versus those from Southern shelters (HR = 3.81, 95% C.I. 1.43–10.14). The effect of estimated adult size, skull type, and age group on adoption were each modified by time in the shelter (p < 0.001). The results of this study indicate that what dogs look like is predictive of their hazard for adoption from shelters, but the effect of some characteristics on hazard for adoption depend on time in the shelter. Further, this study demonstrates that adopters prefer a certain phenotype of shelter dog including those that are puppies, small sized and not brachycephalic, when accounting for time in the sheltering environment.

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

Isogeometric analysis of laminated smart shell structures covered with piezoelectric sensors and actuators using degenerated shell formulation

2019 ◽  
Vol 30 (13) ◽  
pp. 1913-1931 ◽  
Author(s):  
Sajjad Nikoei ◽  
Behrooz Hassani
Keyword(s):  
Single Layer ◽  
Laminated Composite ◽  
Piezoelectric Sensor ◽  
Basis Functions ◽  
Shell Structures ◽  
Free Form ◽  
Control Analysis ◽  
Sensors And Actuators ◽  
Spline Basis ◽  
Shell Formulation

An isogeometric approach to the analysis of laminated composite smart shell structures based on the degenerated formulation and Mindlin–Reissner assumptions using non-uniform rational B-spline basis functions is the subject of this article. To model the laminated orthotropic smart free-form shells, the equivalent single layer theory is adopted, and an accurate approach to construct the local basis systems is used. To consider the electric potential in the piezoelectric layers, a sub-layer approach is employed that assumes linear variation over the thickness of the sub-layer. To investigate the performance of the approach, static, free vibration, and static control analysis of laminated composite shells covered with piezoelectric sensor and actuator layers with different degrees of basis functions is performed. Also, the effect of mechanical loading, various input voltages, and different boundary conditions on the static response and natural frequencies have been investigated. Several numerical examples are presented to demonstrate the efficiency and accuracy of the approach and validated with the existing results from the literature.

THE BOUNDARY FACE METHOD WITH VARIABLE APPROXIMATION BY B-SPLINE BASIS FUNCTION

2012 ◽  
Vol 09 (01) ◽  
pp. 1240009 ◽  
Author(s):  
JINLIANG GU ◽  
JIANMING ZHANG ◽  
XIAOMIN SHENG
Keyword(s):  
Numerical Solutions ◽  
Basis Functions ◽  
Spline Functions ◽  
Well Performance ◽  
Geometric Information ◽  
B Spline ◽  
Numerical Tests ◽  
Boundary Integration ◽  
Spline Basis ◽  
Boundary Face

B-spline basis functions as a new approximation method is introduced in the boundary face method (BFM) to obtain numerical solutions of 3D potential problems. In the BFM, both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces, therefore, keeps the exact geometric information of a body in which the problem is defined. In this paper, local bivariate B-spline functions are proposed to alleviate the influence of B-spline tensor product that will deteriorate the exactness of numerical results. Numerical tests show that the new method has well performance in both exactness and convergence.

Research on the Key Issues of Numerical Controlled Machine Layout Design

2014 ◽  
Vol 548-549 ◽  
pp. 968-973
Author(s):  
Zhi Gang Xu
Keyword(s):  
Recursive Formula ◽  
Layout Design ◽  
Basis Functions ◽  
Nurbs Curve ◽  
B Spline ◽  
Machine Layout ◽  
Spline Basis ◽  
Key Issues ◽  
Normal Vectors

Formulas for the derivatives and normal vectors of non-rational B-spline and NURBS are proved based on de BOOR’s recursive formula. Compared with the existing approaches targeting at the non-rational B-spline basis functions, these equations are directly targeted at the controlling points, so the algorithms and programs for NURBS curve and surface can also be applied to the derivatives and normals, the calculating performance is increased. A simplified equation is also proved in this paper.

Sign in / Sign up

Export Citation Format

Share Document