Inversion of Convex Ordering in the VIX Market

2019 ◽  
Author(s):  
Julien Guyon
Keyword(s):  
Convex Ordering

scholarly journals Convex ordering and quantification of quantumness

2015 ◽  
Vol 90 (7) ◽  
pp. 074024 ◽  
Author(s):  
J Sperling ◽  
W Vogel
Keyword(s):  
Convex Ordering

scholarly journals On the distance between convex-ordered random variables, with applications

2002 ◽  
Vol 34 (2) ◽  
pp. 349-374 ◽  
Author(s):  
Michael V. Boutsikas ◽  
Eutichia Vaggelatou
Keyword(s):  
Random Variables ◽  
Simple Approximation ◽  
Negative Dependence ◽  
Exponential Approximation ◽  
Probability Metrics ◽  
Convex Ordering ◽  
Compound Poisson ◽  
Approximation Techniques ◽  
Negatively Dependent Random Variables ◽  
Dependence Concepts

Simple approximation techniques are developed exploiting relationships between generalized convex orders and appropriate probability metrics. In particular, the distance between s-convex ordered random variables is investigated. Results connecting positive or negative dependence concepts and convex ordering are also presented. These results lead to approximations and bounds for the distributions of sums of positively or negatively dependent random variables. Applications and extensions of the main results pertaining to compound Poisson, normal and exponential approximation are provided as well.

Inversion of convex ordering in the VIX market

2020 ◽  
Vol 20 (10) ◽  
pp. 1597-1623 ◽  
Author(s):  
Julien Guyon
Keyword(s):  
Convex Ordering

Convex ordering of the attained waiting times in single-server queues and related problems

1991 ◽  
Vol 28 (02) ◽  
pp. 433-445 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Genji Yamazaki
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Times ◽  
Service Discipline ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Convex Order ◽  
Convex Ordering ◽  
Single Server Queues ◽  
Service Disciplines

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

On an elementary characterization of the increasing convex ordering, by an application

1994 ◽  
Vol 31 (3) ◽  
pp. 834-840 ◽  
Author(s):  
Armand M. Makowski
Keyword(s):  
Short Proof ◽  
Probability Distributions ◽  
Short Note ◽  
Comparison Result ◽  
Convex Ordering ◽  
Simple Characterization ◽  
Increasing Convex Ordering ◽  
Elementary Characterization

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.

scholarly journals On the distance between convex-ordered random variables, with applications

2002 ◽  
Vol 34 (02) ◽  
pp. 349-374 ◽  
Author(s):  
Michael V. Boutsikas ◽  
Eutichia Vaggelatou
Keyword(s):  
Random Variables ◽  
Simple Approximation ◽  
Negative Dependence ◽  
Exponential Approximation ◽  
Probability Metrics ◽  
Convex Ordering ◽  
Compound Poisson ◽  
Approximation Techniques ◽  
Negatively Dependent Random Variables ◽  
Dependence Concepts

Simple approximation techniques are developed exploiting relationships between generalized convex orders and appropriate probability metrics. In particular, the distance between s-convex ordered random variables is investigated. Results connecting positive or negative dependence concepts and convex ordering are also presented. These results lead to approximations and bounds for the distributions of sums of positively or negatively dependent random variables. Applications and extensions of the main results pertaining to compound Poisson, normal and exponential approximation are provided as well.

Closure of the NBUC class under formation of parallel systems

1993 ◽  
Vol 30 (04) ◽  
pp. 975-978 ◽  
Author(s):  
M. I. Hendi ◽  
A. F. Mashhour ◽  
M. A. Montasser
Keyword(s):  
Parallel Systems ◽  
Convex Ordering ◽  
Distributed Components ◽  
New Better Than Used ◽  
Better Than ◽  
Independent And Identically Distributed

The class of new better than used in convex ordering (NBUC) is shown to be closed under formation of parallel systems with independent and identically distributed components.

Convex ordering criteria for Lévy processes

2007 ◽  
Vol 1 (2) ◽  
pp. 143-173 ◽  
Author(s):  
Jan Bergenthum ◽  
Ludger Rüschendorf
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Convex Ordering
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