scholarly journals Stochastic monotonicity and the Markov product for copulas

2021 ◽  
pp. 125348
Author(s):  
Karl Friedrich Siburg ◽  
Christopher Strothmann
Keyword(s):  
Stochastic Monotonicity

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.

scholarly journals On a Comparison Result for Markov Processes

2008 ◽  
Vol 45 (01) ◽  
pp. 279-286
Author(s):  
Ludger Rüschendorf
Keyword(s):  
Markov Processes ◽  
Comparison Theorem ◽  
General Class ◽  
Stochastic Monotonicity ◽  
Comparison Result ◽  
State Spaces ◽  
Stochastic Orderings ◽  
Infinitesimal Generators ◽  
Real Functions

A comparison theorem is stated for Markov processes in Polish state spaces. We consider a general class of stochastic orderings induced by a cone of real functions. The main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators imply ordering of the processes. Several applications to convex type and to dependence orderings are given. In particular, Liggett's theorem on the association of Markov processes is a consequence of this comparison result.

An Instrumental Variables Design for the Effect of Emergency General Surgery

2018 ◽  
Vol 7 (1) ◽  
Author(s):  
Luke Keele ◽  
Catherine E. Sharoky ◽  
Morgan M. Sellers ◽  
Chris J. Wirtalla ◽  
Rachel R. Kelz
Keyword(s):  
Instrumental Variables ◽  
General Surgery ◽  
Treatment Effect ◽  
Claims Data ◽  
Average Treatment Effect ◽  
Sensitivity Analyses ◽  
Stochastic Monotonicity ◽  
Emergency General Surgery ◽  
Medical Claims ◽  
Operative Care

Abstract Confounding by indication is a critical challenge in evaluating the effectiveness of surgical interventions using observational data. The threat from confounding is compounded when using medical claims data due to the inability to measure risk severity. If there are unobserved differences in risk severity across patients, treatment effect estimates based on methods such a multivariate regression may be biased in an unknown direction. A research design based on instrumental variables offers one possibility for reducing bias from unobserved confounding compared to risk adjustment with observed confounders. This study investigates whether a physician’s preference for operative care is a valid instrumental variable for studying the effect of emergency surgery. We review the plausibility of the necessary causal assumptions in an investigation of the effect of emergency general surgery (EGS) on inpatient mortality among adults using medical claims data from Florida, Pennsylvania, and New York in 2012–2013. In a departure from the extant literature, we use the framework of stochastic monotonicity which is more plausible in the context of a preference-based instrument. We compare estimates from an instrumental variables design to estimates from a design based on matching that assumes all confounders are observed. Estimates from matching show lower mortality rates for patients that undergo EGS compared to estimates based in the instrumental variables framework. Results vary substantially by condition type. We also present sensitivity analyses as well as bounds for the population level average treatment effect. We conclude with a discussion of the interpretation of estimates from both approaches.

Stochastic monotonicity in general queueing networks

1989 ◽  
Vol 26 (02) ◽  
pp. 413-417 ◽  
Author(s):  
J. George Shanthikumar ◽  
David D. Yao
Keyword(s):  
Queueing Networks ◽  
Stochastic Monotonicity ◽  
Jackson Networks ◽  
Monotonicity Properties

We develop a representation for general queueing networks, and study some stochastic monotonicity properties that have been previously established in Jackson networks (e.g. Shanthikumar and Yao (1986), (1987)).

Stochastic Monotonicities in Jackson Queueing Networks

1997 ◽  
Vol 11 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Torgny Lindvall
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Zero Point ◽  
Monotonicity Property ◽  
Stochastic Monotonicity ◽  
Property A ◽  
Jackson Network ◽  
Queueing Process ◽  
Network Process ◽  
Number Of Customers

When starting from 0, a standard M/M/k queueing process has a second-order stochastic monotonicity property of a strong kind: its increments are stochastically decreasing (the SDI property). A first attempt to generalize this to the Jackson queueing network fails. This gives us reason to reexamine the underlying theory for stochastic monotonicity of Markov processes starting from a zero-point, in order to find a condition on a function of a Jackson network process to have the SDI property. It turns out that the total number of customers at time t has the desired property, if the network is idle at time O. We use couplings in our analysis; they are also of value in the comparison of two networks with different parameters.

Stochastic monotonicity and queues subject to tidal interruptions

1971 ◽  
Vol 70 (1) ◽  
pp. 61-75 ◽  
Author(s):  
J. C. Gittins
Keyword(s):  
Integral Equation ◽  
Approximate Solutions ◽  
Stochastic Monotonicity ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Waiting Line

AbstractA generalization is given of the notion of stochastic monotonicity. This is used in setting up, and showing how to obtain approximate solutions for, an integral equation formulation of GI/G/l queues, when access to the waiting-line is subject to periodic interruptions.

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