Closed Form Formula For Undertaking Specific Parameters Calculation Under Solvency II

2017 ◽  
Author(s):  
Filippo Siegenthaler
Keyword(s):  
Closed Form ◽  
Solvency Ii ◽  
Closed Form Formula ◽  
Parameters Calculation

scholarly journals ON THE REPRESENTATION OF THE NESTED LOGIT MODEL

2021 ◽  
pp. 1-11
Author(s):  
Alfred Galichon
Keyword(s):  
Closed Form ◽  
Logit Model ◽  
Random Variables ◽  
Nested Logit ◽  
Random Utility ◽  
Nested Logit Model ◽  
Utility Representation ◽  
Phd Thesis ◽  
Closed Form Formula

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

A Closed-Form Formula of Radiation and Total Efficiency for Lossy Multiport Antennas

2019 ◽  
Vol 18 (12) ◽  
pp. 2468-2472
Author(s):  
Min Wang ◽  
Tian-Hong Loh ◽  
Yongjiu Zhao ◽  
Qian Xu
Keyword(s):  
Closed Form ◽  
Total Efficiency ◽  
Closed Form Formula ◽  
Multiport Antennas

ON COMPUTING KAUFFMAN BRACKET POLYNOMIAL OF MONTESINOS LINKS

2010 ◽  
Vol 19 (08) ◽  
pp. 1001-1023 ◽  
Author(s):  
XIAN'AN JIN ◽  
FUJI ZHANG
Keyword(s):  
Closed Form ◽  
Explicit Expression ◽  
Computer Algebra ◽  
Jones Polynomial ◽  
Kauffman Bracket ◽  
Jones Polynomials ◽  
Bracket Polynomial ◽  
Bracket Polynomials ◽  
Closed Form Formula

It is well known that Jones polynomial (hence, Kauffman bracket polynomial) of links is, in general, hard to compute. By now, Jones polynomials or Kauffman bracket polynomials of many link families have been computed, see [4, 7–11]. In recent years, the computer algebra (Maple) techniques were used to calculate link polynomials for various link families, see [7, 12–14]. In this paper, we try to design a maple program to calculate the explicit expression of the Kauffman bracket polynomial of Montesinos links. We first introduce a family of "ring of tangles" links, which includes Montesinos links as a special subfamily. Then, we provide a closed-form formula of Kauffman bracket polynomial for a "ring of tangles" link in terms of Kauffman bracket polynomials of the numerators and denominators of the tangles building the link. Finally, using this formula and known results on rational links, the Maple program is designed.

Closed-form formula of magnetic gradient tensor for a homogeneous polyhedral magnetic target: A tetrahedral grid example

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. WB21-WB28 ◽  
Author(s):  
Zhengyong Ren ◽  
Chaojian Chen ◽  
Jingtian Tang ◽  
Huang Chen ◽  
Shuanggui Hu ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Magnetization Vector ◽  
Gradient Tensor ◽  
Magnetic Gradient ◽  
Closed Form Solutions ◽  
Tetrahedral Grid ◽  
Pipeline Model ◽  
The Magnetic Field ◽  
Closed Form Formula

A closed-form formula is developed for the full magnetic gradient tensor of a polyhedral body with a homogeneous magnetization vector. It is based on the direct derivative technique on the closed form of the magnetic field. These analytical expressions are implemented into an easy-to-use C++ package which simultaneously calculates the magnetic potential, the magnetic field, and the full magnetic gradient tensor for magnetic targets. Modern unstructured tetrahedral grids are adopted to represent the polyhedral body so that our code can deal with arbitrarily complicated magnetic targets. A prismatic body is tested to verify the accuracies of our closed-form formula. Excellent agreements are obtained between our closed-form solutions and solutions of a prismatic magnetic body with differences up to machine precision. A pipeline model is used to demonstrate its capability to deal with complicated magnetic targets. This C++ code is freely available to the magnetic exploration community.

AN IMPROVED APPROACH TO EVALUATE DEFAULT PROBABILITIES AND DEFAULT CORRELATIONS WITH CONSISTENCY

2016 ◽  
Vol 19 (05) ◽  
pp. 1650036 ◽  
Author(s):  
WEIPING LI ◽  
TIM KREHBIEL
Keyword(s):  
Risk Management ◽  
Closed Form ◽  
First Passage Time ◽  
Passage Time ◽  
Default Probability ◽  
Default Correlation ◽  
First Passage ◽  
Management Implications ◽  
Asset Correlation ◽  
Closed Form Formula

We provide (i) a simplified analytic closed form formula for evaluating joint default probability, (ii) an improved method to resolve the inconsistency between the univariate process underlying firm-specific default probability and the correlated bivariate process of the first-passage-time default correlation model, (iii) illustration of risk management implications from misspecification of the default state space. Our closed form formula provides a natural extension of previous structural first-passage-time models and shows the sensitivities of default correlation numerically with respect to the underlying asset correlation, obligor credit quality and time horizon. We emphasize the disparate credit risk management implications of our result in contrast to commonly used risk measurement methods.

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