Peacocks Obtained by Normalisation: Strong and Very Strong Peacocks

Bogso, Antoine-Marie; Profeta, Christophe; Roynette, Bernard

doi:10.1007/978-3-642-27461-9_16

Cited by 2 publications

(4 citation statements)

References 16 publications

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“…Observe that h is a non-increasing C 1 -class function.Indeed, the tail m of Y is a non-increasing C 1 -class function and g is a non-decreasing C 1 -class function. Moreover, we deduce from(4…”

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confidence: 92%

MRL order, log-concavity and an application to peacocks

Bogso

2015

Stochastic Processes and their Applications

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Highlights• We recall some properties of R + -valued homogeneous Markov processes which admit a totally positive transition kernel.• We establish the equivalence between the MRL ordering and a log-concavity type condition.• We exhibit new classes of MRL processes, i.e. integrable processes which increase in the MRL order. AbstractWe provide an equivalent log-concavity condition to the mean residual life (MRL) ordering for realvalued processes. This result, combined with classical properties of total positivity of order 2, allows to exhibit new families of integrable processes which increase in the MRL order (MRL processes). Note that MRL processes with constant mean are peacocks to which the Azéma-Yor (Skorokhod embedding) algorithm yields an explicit associated martingale.

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confidence: 92%

MRL order, log-concavity and an application to peacocks

Bogso

2015

Stochastic Processes and their Applications

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“…Since E[N t ] does not depend on t (which is a necessary condition to be a peacock), it is natural to look for processes (V t , t ≥ 0) for which (N t , t ≥ 0) is a peacock. Many examples of such processes are presented in [6]. Note that if V t := t 0 e Bs− s 2 ds, then (CEX08) is equivalent to:…”

Section: E[|vmentioning

confidence: 99%

“…For this reason, we call peacocks with respect to maturity peacocks of type N 1 and peacocks with respect to volatility peacocks of type N 2 . For processes of type N 1 , a partial answer to (Q) is given in [6] when X has independent and log-concave increments. We extend this result to real valued processes which satisfy (SCM).…”

Section: E[|vmentioning

confidence: 99%

“…Inspired by Carr-Ewald-Xiao and Baker-Yor results, the authors of [18] exhibited several examples of peacocks and they provided several methods to associate explicitely martingales to certain of them. We refer the reader to [32], [17], [3], [8] and [6] for further interesting results about peacock processes. In this paper, we exibit new families of peacocks using multivariate total positivity theory.…”

Section: Introductionmentioning

confidence: 99%

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An application of multivariate total positivity to peacocks

Bogso

2014

ESAIM: PS

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Abstract:We use multivariate total positivity theory to exhibit new families of peacocks. As ). There are many random vectors which are strongly conditionally monotone (SCM). Indeed, we shall prove that multivariate totally positive of order 2 (MTP 2 ) random vectors are SCM. As a consequence, stochastic processes with MTP 2 finite-dimensional marginals are SCM. This family includes processes with independent and log-concave increments, and one-dimensional diffusions which have absolutely continuous transition kernels.Key words: convex order, peacocks, total positivity of order 2 (TP 2 ), multivariate total positivity of order 2 (MTP 2 ), Markov property, strong conditional monotonicity.

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Peacocks Obtained by Normalisation: Strong and Very Strong Peacocks

Cited by 2 publications

References 16 publications

MRL order, log-concavity and an application to peacocks

MRL order, log-concavity and an application to peacocks

An application of multivariate total positivity to peacocks

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