Dynamic programming with shape-preserving rational spline Hermite interpolation

2012 ◽  
Vol 117 (1) ◽  
pp. 161-164 ◽  
Author(s):  
Yongyang Cai ◽  
Kenneth L. Judd
Keyword(s):  
Dynamic Programming ◽  
Hermite Interpolation ◽  
Shape Preserving ◽  
Rational Spline

scholarly journals A new method for interpolating yield curve data, with applications to the South African market

2013 ◽  
Vol 16 (4) ◽  
pp. 395-406 ◽  
Author(s):  
Paul Du Preez ◽  
Eben Mare
Keyword(s):  
South African ◽  
Hermite Interpolation ◽  
Yield Curve ◽  
New Method ◽  
The South ◽  
Shape Preserving ◽  
Interpolation Methods ◽  
Work Done

This paper presents a method for interpolating yield curve data in a manner that ensures positive and continuous forward curves. As shown by Hagan and West (2006), traditional interpolation methods suffer from problems: they posit unreasonable expectations, or are not necessarily arbitrage-free. The method presented in this paper, which we refer to as the “monotone preserving r(t)t  method", stems from the work done in the field of shape preserving cubic Hermite interpolation, by authors such as Akima (1970), de Boor and Swartz (1977), and Fritsch and Carlson (1980). In particular, the monotone preserving r(t)t method applies shape preserving cubic Hermite interpolation to the log capitalisation function. We present some examples of South African swap and bond curves obtained under the monotone preserving  r(t)t method. 

Shape-preserving dynamic programming

2012 ◽  
Vol 77 (3) ◽  
pp. 407-421 ◽  
Author(s):  
Yongyang Cai ◽  
Kenneth L. Judd
Keyword(s):  
Dynamic Programming ◽  
Shape Preserving

PiecewiseC 1-shape-preserving Hermite interpolation

Computing ◽  
1996 ◽  
Vol 56 (4) ◽  
pp. 323-341 ◽  
Author(s):  
C. Conti ◽  
R. Morandi
Keyword(s):  
Hermite Interpolation ◽  
Shape Preserving

scholarly journals Estimating Gini Coefficient from Grouped Data Based on Shape-Preserving Cubic Hermite Interpolation of Lorenz Curve

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2551
Author(s):  
Songpu Shang ◽  
Songhao Shang
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Strain Energy ◽  
Hermite Interpolation ◽  
Interpolation Method ◽  
Grouped Data ◽  
Shape Preserving ◽  
Unequally Spaced ◽  
Interpolation Curve ◽  
The Lorenz Curve

The Lorenz curve and Gini coefficient are widely used to describe inequalities in many fields, but accurate estimation of the Gini coefficient is still difficult for grouped data with fewer groups. We proposed a shape-preserving cubic Hermite interpolation method to approximate the Lorenz curve by maximizing or minimizing the strain energy or curvature variation energy of the interpolation curve, and a method to estimate the Gini coefficient directly from the coefficients of the interpolation curve. This interpolation method can preserve the essential requirements of the Lorenz curve, i.e., non-negativity, monotonicity, and convexity, and can estimate the derivatives at intermediate points and endpoints at the same time. These methods were tested with 16 grouped quintiles or unequally spaced datasets, and the results were compared with the true Gini coefficients calculated with all census data and results estimated with other methods. Results indicate that the maximum strain energy interpolation method generally performs the best among different methods, which is applicable to both equally and unequally spaced grouped datasets with higher precision, especially for grouped data with fewer groups.

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