The Properties Related to the Moment Generating Function of the Fuzzy Variable

2014 ◽  
Vol 519-520 ◽  
pp. 863-866
Author(s):  
Sheng Ma
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Uncertainty Theory ◽  
Fuzzy Variable ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Moment Generating Functions ◽  
The Moment

In the paper, some properties related to the moment generating function of a fuzzy variable are discussed based on uncertainty theory. And we obtain the result that the convergence of moment generating functions to an moment generating function implies convergence of credibility distribution functions. Thats, the moment generating function characterizes a credibility distribution.

Bounds for moment generating functions and for extinction probabilities

1966 ◽  
Vol 3 (1) ◽  
pp. 171-178 ◽  
Author(s):  
D. Brook
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Natural Extension ◽  
Random Variable ◽  
Moment Generating Function ◽  
Multivariate Case ◽  
Extinction Probabilities ◽  
Moment Generating Functions

Suppose that we have a non-negative, real valued random variable x, whose distribution is governed by some unknown moment generating function M(t). Suppose further that we are given certain moments of x, then the question to be discussed in this paper is : can we find a sharp upper bounding function for the m.g.f.? It will be shown that this is usually possible both in the single variate case and in its natural extension to the multivariate case.

scholarly journals Smile Asymptotics II: Models with Known Moment Generating Functions

2008 ◽  
Vol 45 (1) ◽  
pp. 16-32 ◽  
Author(s):  
Shalom Benaim ◽  
Peter Friz
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Implied Volatility ◽  
Moment Generating Function ◽  
Tail Asymptotics ◽  
Volatility Smile ◽  
Tauberian Conditions ◽  
Black Scholes ◽  
Moment Generating Functions ◽  
Exponential Lévy Models

The tail of risk neutral returns can be related explicitly with the wing behaviour of the Black-Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we establish, under easy-to-check Tauberian conditions, tail asymptotics on logarithmic scales. Such asymptotics are enough to make the tail-wing formula (see Benaim and Friz (2008)) work and so we obtain, under generic conditions, a limiting slope when plotting the square of the implied volatility against the log strike, improving a lim sup statement obtained earlier by Lee (2004). We apply these results to time-changed exponential Lévy models and examine several popular models in more detail, both analytically and numerically.

Bounds for moment generating functions and for extinction probabilities

1966 ◽  
Vol 3 (01) ◽  
pp. 171-178 ◽  
Author(s):  
D. Brook
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Natural Extension ◽  
Random Variable ◽  
Moment Generating Function ◽  
Multivariate Case ◽  
Extinction Probabilities ◽  
Moment Generating Functions

Suppose that we have a non-negative, real valued random variable x, whose distribution is governed by some unknown moment generating function M(t). Suppose further that we are given certain moments of x, then the question to be discussed in this paper is : can we find a sharp upper bounding function for the m.g.f.? It will be shown that this is usually possible both in the single variate case and in its natural extension to the multivariate case.

scholarly journals Smile Asymptotics II: Models with Known Moment Generating Functions

2008 ◽  
Vol 45 (01) ◽  
pp. 16-32 ◽  
Author(s):  
Shalom Benaim ◽  
Peter Friz
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Implied Volatility ◽  
Moment Generating Function ◽  
Tail Asymptotics ◽  
Volatility Smile ◽  
Tauberian Conditions ◽  
Black Scholes ◽  
Moment Generating Functions ◽  
Exponential Lévy Models

The tail of risk neutral returns can be related explicitly with the wing behaviour of the Black-Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we establish, under easy-to-check Tauberian conditions, tail asymptotics on logarithmic scales. Such asymptotics are enough to make the tail-wing formula (see Benaim and Friz (2008)) work and so we obtain, under generic conditions, a limiting slope when plotting the square of the implied volatility against the log strike, improving a lim sup statement obtained earlier by Lee (2004). We apply these results to time-changed exponential Lévy models and examine several popular models in more detail, both analytically and numerically.

scholarly journals Distribution Function, Probability Generating Function and Archimedean Generator

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2108
Author(s):  
Weaam Alhadlaq ◽  
Abdulhamid Alzaid
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Generating Functions ◽  
Probability Generating Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Archimedean Copulas ◽  
Cumulative Distribution Functions ◽  
Probability Generating Functions ◽  
Real Functions

Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that under certain conditions the cumulative distribution functions on (0, 1) and probability generating functions can be used as Archimedean generators. It is shown that most of the well-known Archimedean copulas can be generated using such distributions. Further, we introduced new Archimedean copulas.

Problèmes de premier passage résolubles par la méthode de séparation des variables

1995 ◽  
Vol 32 (02) ◽  
pp. 337-348
Author(s):  
Mario Lefebvre
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Generating Function ◽  
Moment Generating Function ◽  
First Passage Times ◽  
Standard Brownian Motion ◽  
First Passage ◽  
The Moment ◽  
Passage Times

In this paper, bidimensional stochastic processes defined by ax(t) = y(t)dt and dy(t) = m(y)dt + [2v(y)]1/2 dW(t), where W(t) is a standard Brownian motion, are considered. In the first section, results are obtained that allow us to characterize the moment-generating function of first-passage times for processes of this type. In Sections 2 and 5, functions are computed, first by fixing the values of the infinitesimal parameters m(y) and v(y) then by the boundary of the stopping region.

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