Stein's Lemma for elliptical random vectors
By Zinoviy Landsman, Johana Nešlehová. 2008
78 citations recorded by the source corpus.
For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.
Subfields: Economics and Econometrics, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/5486f50f5b853d0569eea4e61045573ef731582f
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Citations in the corpus
- Exponential convergence rates for Batch Normalization: The power of length-direction decoupling in non-convex optimization (2018, methodology): “…random variable distributed with mean Under the above assumption we have that for a differentiable function g ( z ) : R d → R the following equality holds This result, which can be derived using a simple application of integration by parts, is called Stein’s lemma (Landsman and Ne v slehov´a, 2008).”
- Multi-asset portfolio optimization and out-of-sample performance: an evaluation of Black–Litterman, mean-variance, and naïve diversification approaches (2017, unknown): “Although this seems to be a critical assumption, Landsman and Nešlehová (2008) show that it is sufficient that returns are elliptically symmetrically distributed so that all investor preferences are equivalent to mean-variance preferences.”
- Weighted Pricing Functionals With Applications to Insurance (2009, methodology): “For extensions of Stein’s lemma to elliptical distributions, see Landsman and Nešlehová (2008) as well as the references therein.”
- Weighted Risk Capital Allocations (2008, unknown): “Since any of the two requirements may not be desirable, Landsman (2006), and Landsman and Neolehova (2008) have relaxed the normality assumption by establishing an extension of Stein’s Lemma for elliptical distributions.”