Random integral representations for free-infinitely divisible and tempered stable distributions

2007 ◽  
Vol 77 (4) ◽  
pp. 417-425 ◽  
Author(s):  
Zbigniew J. Jurek
Keyword(s):  
Stable Distributions ◽  
Integral Representations ◽  
Infinitely Divisible ◽  
Tempered Stable Distributions ◽  
Random Integral

scholarly journals Asymmetrically tempered stable distributions with applications to finance

2019 ◽  
Vol 39 (1) ◽  
pp. 85-98
Author(s):  
A. Arefi ◽  
R. Pourtaheri
Keyword(s):  
Lévy Processes ◽  
Stable Distributions ◽  
Levy Processes ◽  
Infinitely Divisible ◽  
Financial Modeling ◽  
New Family ◽  
Tempered Stable Distributions ◽  
Exponential Lévy Models

In this paper, we introduce a technique to produce a new family of tempered stable distributions. We call this family asymmetrically tempered stable distributions.We provide two examples of this family named asymmetrically classical modified tempered stable ACMTS and asymmetrically modified classical tempered stable AMCTS distributions. Since the tempered stable distributions are infinitely divisible, Levy processes can be induced by the ACMTS and AMCTS distributions. The properties of these distributions will be discussed along with the advantages in applying them to financial modeling. Furthermore, we develop exponential Levy models for them. To demonstrate the advantages of the exponential Levy ACMTS and AMCTS models, we estimate parameters for the S&P 500 Index.

Conditionally free semi-stable distributions

2015 ◽  
Vol 18 (02) ◽  
pp. 1550015
Author(s):  
Anna Dorota Krystek ◽  
Łukasz Jan Wojakowski
Keyword(s):  
Free Probability ◽  
Stable Distributions ◽  
Infinitely Divisible ◽  
Stable Measures

We define a notion of semi–stability in the conditionally free probability and explain that the semi–stable measures are infinitely divisible. We also show that in the conditionally free probability stable measures are semi–stable, and that semi–stability for all r implies stability.

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