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Multivariate extensions of expectiles risk measures

100%

Maume-Deschamps V., Rullière D., Said K.

Dependence Modeling

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2017

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tom 5

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nr 1

20-44

EN

This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.

2

Pressure and recurrence

100%

Maume-Deschamps V., Schmitt B., Urbański M., Zdunik A.

Fundamenta Mathematicae

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2003

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tom 178

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nr 2

129-141

EN

We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) $lim_{n→∞} n^{-1} log ∑_{j=0}^{τₙ(x)} μ(αⁿ(T^j(x)))$, where $αⁿ(T^j(x))$ is the element of the partition containing $T^j(x)$ and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).

3

Invariant measures for piecewise convex transformations of an interval

100%

Bose C., Maume-Deschamps V., Schmitt B., Shin S.

Studia Mathematica

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2002

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tom 152

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nr 3

263-297

EN

We investigate the existence and ergodic properties of absolutely continuous invariant measures for a class of piecewise monotone and convex self-maps of the unit interval. Our assumption entails a type of average convexity which strictly generalizes the case of individual branches being convex, as investigated by Lasota and Yorke (1982). Along with existence, we identify tractable conditions for the invariant measure to be unique and such that the system has exponential decay of correlations on bounded variation functions and Bernoulli natural extension. In the case when there is more than one invariant density we identify a dominant component over which the above properties also hold. Of particular note in our investigation is the lack of smoothness or uniform expansiveness assumptions on the map or its powers.

Ograniczanie wyników

1 Dependence Modeling

1 Fundamenta Mathematicae

1 Studia Mathematica

3 Maume-Deschamps V.

2 Schmitt B.

1 Bose C.

1 Rullière D.

1 Said K.

1 Shin S.

1 Urbański M.

1 Zdunik A.

1 2017

1 2003

1 2002

Multivariate extensions of expectiles risk measures

Pressure and recurrence

Invariant measures for piecewise convex transformations of an interval