We study irreducible time-homogenous Markov chains with finite state space in
discrete time. We obtain results on the sensitivity of the stationary
distribution and other statistical quantities with respect to perturbations of
the transition matrix. We define a new closeness relation between transition
matrices, and use graph-theoretic techniques, in contrast with the matrix
analysis techniques previously used.Comment: 22 page

Barlow

Cohen

Fabio Spizzichino

Gudder

Hardcastle

Kimeldorf

Marco Scarsini

Samuels

Shaked

Simpson

Vaupel

English

arXiv

SCARSINI, MARCO

SPIZZICHINO F.

Archivio della ricerca- LUISS Libera Università Internazionale degli Studi Sociali Guido Carli di Roma

Simpson-type paradoxes, dependence, and ageing

Consider random vectors formed by a finite number of independent groups of i.i.d. random variables, where those of the last group are stochastically smaller than those of the other groups. Conditions are given such that certain functions, defined as suitable means of supermodular functions of the random variables of the vectors, are supermodular or increasing directionally convex. Comparisons based on the increasing convex order of supermodular functions of such random vectors are also investigated. Applications of the above results are then provided in risk theory, queueing theory, and reliability theory, with reference to (i) net stop-loss reinsurance premiums of portfolios from different groups of insureds, (ii) closed cyclic multiclass Gordon-Newell queueing networks, and (iii) reliability of series systems formed by units selected from different batche

Di Crescenzo, A.

Frostig, E.

Pellerey, Franco

PORTO Publications Open Repository TOrino

An Introduction to Queueing Theory and MatrixAnalytic Methods.

Closed queueing systems with exponential servers.

Comparison of increasing directionally convex transformations of random vectors with a common copula.

Convex comparisons for random sums in random environments and applications.

Dependence properties and bounds for ruin probabilities in multivariate compound risk models.

Foundations of Mathematical Economics.

Improving series and parallel systems through mixtures of duplicated dependent components. Naval Res.

Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data.

Inequalities for stochastic models via supermodular orderings.

Inequalities: Theory of Majorization and its Applications.

Mathematical Theory of Reliability. With contributions by

Modeling and comparing dependencies in multivariate risk portfolios.

Monotone methods for Markovian equilibrium in dynamic economies. Stochastic equilibrium problems in economics and game theory.

Monotonicity and supermodularity results for the Erlang loss system.

Portfolio selection problems via the bivariate characterization of stochastic domince relations.

Regularity of stochastic processes. A theory based on directional convexity.

Stochastic convexity on general space.

Stochastic Orders.

Stop-loss order for portfolios of dependent risks.

Supermodular comparison of time-to-ruin random vectors.

Stochastic Comparisons of Symmetric Supermodular Functions of Heterogeneous Random Vectors

Consider random vectors formed by a finite number of independent groups
of i.i.d. random variables, where those of the last group are stochastically
smaller than those of the other groups. Conditions are given such that certain functions, defined as suitable means of supermodular functions of the random variables of the vectors, are supermodular or increasing directionally convex. Comparisons based on the increasing convex order of supermodular functions of such random vectors are also investigated. Applications of the above results are then provided in risk theory, queueing theory, and reliability theory, with reference to (i) net stop-loss reinsurance premiums of portfolios from different groups of insureds, (ii) closed cyclic multiclass Gordon-Newell queueing networks, and (iii) reliability of series systems formed by units selected from different batches

Di Crescenzo A.

Frostig E.

PELLEREY, FRANCO

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

We consider the problem of stochastic comparison of general GARCH-like processes for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the GARCH process itself, and we discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the GARCH process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular orders. Finally, we discuss ordering with respect to the parameters in the GARCH(1, 1) case.</jats:p

Fabio Bellini

Franco Pellerey

Carlo Sgarra

Salimeh Yasaei Sekeh

Crossref

Journal of Applied Probability

Comparison Results for GARCH Processes

Consider random vectors formed by a finite number of independent groups of i.i.d.\ random variables,
where those of the last group are stochastically smaller than those of the other groups.
Conditions are given such that certain functions, defined as suitable means of
supermodular functions of the random variables of the vectors, are supermodular
or increasing directionally convex. Comparisons based on the increasing convex
order of supermodular functions of such random vectors are also investigated.
Applications of the above results are then provided in risk theory, queueing theory,
and reliability theory, with reference to
(i) net stop-loss reinsurance premiums of portfolios from different groups of insureds,
(ii) closed cyclic multiclass Gordon-Newell queueing networks, and
(iii) reliability of series systems formed by units selected from different batches

DI CRESCENZO, Antonio

Esther Frostig

Archivio della Ricerca - Università di Salerno

Stochastic comparisons of symmetric supermodular functions of heterogeneous random vectors

This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black-Scholes model and Kou's double exponential jump diffusion model. By establishing a relationship between floating- and fixed-strike quantile option prices, we can also apply this pricing and hedging method to floating-strike quantile options. Numerical experiments demonstrate that our pricing and hedging method is fast, stable, and accurate.</jats:p

Ning Cai

Pricing and Hedging of Quantile Options in a Flexible Jump Diffusion Model

CiteSeerX

Comparison Results for Garch Processes

We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used

Vieille, Nicolas

Solan, Eilon

Hal-Diderot

Perturbed Markov chains

Consider random vectors formed by a finite number of independent groups of independent and identically distributed random variables, where those of the last group are stochastically smaller than those of the other groups. Conditions are given such that certain functions, defined as suitable means of supermodular functions of the random variables of the vectors, are supermodular or increasing directionally convex. Comparisons based on the increasing convex order of supermodular functions of such random vectors are also investigated. Applications of the above results are then provided in risk theory, queueing theory, and reliability theory, with reference to (i) net stop-loss reinsurance premiums of portfolios from different groups of insureds, (ii) closed cyclic multiclass Gordon-Newell queueing networks, and (iii) reliability of series systems formed by units selected from different batches.</jats:p

Antonio Di Crescenzo

A diffusion with a discontinuous local time.

A generalized TaylorAris formula and skew diffusion.

A note on the theoretical foundations of particle tracking methods in heterogeneous porous media.

A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients.

An introduction to probability theory and its applications.

Asymmetric skew Bessel processes and their applications to finance.

Brownian motions on a half line.

Edge-Mediated Dispersal Behavior in a Prairie Butterfly. Ecology,

Effect of environmental variability on habitat selection, diet, provisioning behaviour and chick growth in yellow-nosed albatrosses.

First passage time analysis of animal movement and insights into the functional response.

Fitting probability distributions to animal Skew Brownian Motion 17 movement trajectories: using artificial neural networks to link distance, resources, and memory.

Fractal Analyses of Animal Movement: A Critique.

Invariance principles for ranked excursion lengths and heights.

Laboratory experiments on dispersive transport across interfaces: The role of flow direction.

Le “Skew-Brownian motion” et les processus qui en de´rivent.

Multi-skew Brownian motion and diffusion in layered media.

Occupation and Local Times for Skew Brownian Motion with Applications to Dispersion Across an Interface.

On skew Brownian motion. The Annals of Probability,

On Skewness in Breakthrough Curves Due to Solute Transport Across an Interface. Water Resour.

On the distribution of ranked heights of excursions of a brownian bridge. The Annals of Probability,

One-dimensional stochastic differential equations involving the local times of the unknown process.

Random diffusion models for animal movement.

Scaling of landscapes in landscape ecology, or, landscape ecology from a beetle’s perspective.

Stochastic processes with applications.

The transition zone chlorophyll front, a dynamic global feature defining migration and forage habitat for marine resources.

Translating Foraging Movements in Heterogeneous Environments into the Spatial Distribution of Foragers.

Using first-passage time in the analysis of area-restricted search and habitat selection.

Perturbed Markov Chains

Perturbed Markov Chains

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Archivio della ricerca- LUISS Libera Università Internazionale degli Studi Sociali Guido Carli di Roma

PORTO Publications Open Repository TOrino

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

Crossref

Archivio della Ricerca - Università di Salerno

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CiteSeerX

Hal-Diderot

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