Statistics of Random Processes I

Liptser, R.; Shiryayev, A. N.

doi:10.1007/978-1-4757-1665-8

Cited by 1,138 publications

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“…Then, as it is well-known (see, e.g., Liptser and Shiryaev [23]), for each α ∈ A the equation (2.1) has an unique strong solution Y ε (α) = (Y ε s (α)) 0≤s≤t , and in addition (see Kutoyants [17])…”

Section: Introduction Motivation and Resultsmentioning

confidence: 75%

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Optimal robust mean-variance hedging in incomplete financial markets

Lazrieva

Toronjadze

2008

J Math Sci

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Abstract. Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary information structure and misspecified volatility of asset price, which is modelled by multidimensional continuous semimartingale. Obtained results are applied to stochastic volatility model, where the model of latent volatility process contains unknown multidimensional parameter in drift coefficient and small parameter in diffusion term.

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Section: Introduction Motivation and Resultsmentioning

confidence: 75%

“…Under some technical assumptions (see Proposition 5.1 of RT [32], and Bujeux and Rochet [23] for general diffusion of volatility process)…”

Section: Introduction Motivation and Resultsmentioning

confidence: 99%

Optimal robust mean-variance hedging in incomplete financial markets

Lazrieva

Toronjadze

2008

J Math Sci

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“…Then, taking the expectations with respect to the probability measure P t,φ in (5.6), by means of the optional sampling theorem (see, e.g. [26,Chapter III,Theorem 3.6] or [24, Chapter I, Theorem 3.22]), we get the inequalities…”

Section: Appendixmentioning

confidence: 99%

On the sequential testing and quickest change-point detection problems for Gaussian processes

Gapeev

Stoev

2017

Stochastics

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We study the sequential hypothesis testing and quickest change-point (disorder) detection problems with linear delay penalty costs for certain observable time-inhomogeneous Gaussian diffusions and fractional Brownian motions. The method of proof consists of the reduction of the initial problems into the associated optimal stopping problems for onedimensional time-inhomogeneous diffusion processes and the analysis of the associated free boundary problems for partial differential operators. We derive explicit estimates for the Bayesian risk functions and optimal stopping boundaries for the associated weighted likelihood ratios and obtain their exact asymptotic growth rates under large time values.

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“…It is also seen from (2.5) that Π is a (time-homogeneous strong) Markov process with respect to its natural filtration, which obviously coincides with (ℱ ) ≥0 . It also follows from [25;Theorem 9.3] that the process Π = (Π ) ≥0 defined by Π = (Θ = , Θ 0 = | ℱ ), for = 0, 1, solves the stochastic differential equation:…”

Section: Sufficient Statisticsmentioning

confidence: 99%

Bayesian Switching Multiple Disorder Problems

Gapeev

2016

Mathematics of OR

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This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it. Bayesian switching multiple disorder problemsPavel V. Gapeev * To appear in Mathematics of Operations ResearchThe switching multiple disorder problem seeks to determine an ordered infinite sequence of times of alarms which are as close as possible to the unknown times of disorders, or change-points, at which the observable process changes its probability characteristics. We study a Bayesian formulation of this problem for an observable Brownian motion with switching constant drift rates. The method of proof is based on the reduction of the initial problem to an associated optimal switching problem for a three-dimensional diffusion posterior probability process and the analysis of the equivalent coupled parabolic-type free-boundary problem. We derive analytic-form estimates for the Bayesian risk function and the optimal switching boundaries for the components of the the posterior probability process.

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Statistics of Random Processes I

Cited by 1,138 publications

References 0 publications

Optimal robust mean-variance hedging in incomplete financial markets

Optimal robust mean-variance hedging in incomplete financial markets

On the sequential testing and quickest change-point detection problems for Gaussian processes

Bayesian Switching Multiple Disorder Problems

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