Stochastic monotonicity of a distribution family associated with matrix projections and its application

2020 ◽  
pp. 1-11
Author(s):  
Xiaomi Hu ◽  
Yufei Wang
Keyword(s):  
Stochastic Monotonicity ◽  
Distribution Family

scholarly journals Stochastic orders for a multivariate Pareto distribution

2021 ◽  
Vol 29 (1) ◽  
pp. 53-69
Author(s):  
Luigi-Ionut Catana
Keyword(s):  
Pareto Distribution ◽  
Random Variables ◽  
Stochastic Orders ◽  
Distribution Family ◽  
Theoretical Results

Abstract In this article we give some theoretical results for equivalence between different stochastic orders of some kind multivariate Pareto distribution family. Weak multivariate orders are equivalent or imply different stochastic orders between extremal statistics order of two random variables sequences. The random variables in this article are not neccesary independent.

scholarly journals AN ADAPTIVE TEST OF STOCHASTIC MONOTONICITY

2020 ◽  
pp. 1-42
Author(s):  
Denis Chetverikov ◽  
Daniel Wilhelm ◽  
Dongwoo Kim
Keyword(s):  
Monte Carlo ◽  
Conditional Distribution ◽  
Asymptotic Properties ◽  
Nonparametric Test ◽  
Critical Value ◽  
Data Driven ◽  
Local Alternatives ◽  
Stochastic Monotonicity ◽  
Adaptive Test ◽  
Finite Samples

We propose a new nonparametric test of stochastic monotonicity which adapts to the unknown smoothness of the conditional distribution of interest, possesses desirable asymptotic properties, is conceptually easy to implement, and computationally attractive. In particular, we show that the test asymptotically controls size at a polynomial rate, is nonconservative, and detects certain smooth local alternatives that converge to the null with the fastest possible rate. Our test is based on a data-driven bandwidth value and the critical value for the test takes this randomness into account. Monte Carlo simulations indicate that the test performs well in finite samples. In particular, the simulations show that the test controls size and, under some alternatives, is significantly more powerful than existing procedures.

scholarly journals Stochastic Monotonicity and Duality ofkth Order with Application to Put-Call Symmetry of Powered Options

2015 ◽  
Vol 52 (1) ◽  
pp. 82-101 ◽  
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Option Pricing ◽  
Markov Processes ◽  
Ruin Probability ◽  
Analytic Approach ◽  
Stochastic Monotonicity ◽  
Full Characterization

We introduce a notion ofkth order stochastic monotonicity and duality that allows us to unify the notion used in insurance mathematics (sometimes refereed to as Siegmund's duality) for the study of ruin probability and the duality responsible for the so-called put-call symmetries in option pricing. Our generalkth order duality can be interpreted financially as put-call symmetry for powered options. The main objective of this paper is to develop an effective analytic approach to the analysis of duality that will lead to the full characterization ofkth order duality of Markov processes in terms of their generators, which is new even for the well-studied case of put-call symmetries.

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