Abstract
In this paper, we consider a random vector $$X=\left( X_1,X_2\right) $$ following a multivariate Skew Normal distribution and we provide an explicit formula for the expected value of X conditioned to the event $$X \le \overline{X}$$, with $$\overline{X} \in \mathbb {R}^2$$. Such a conditional expectation has an intuitive interpretation in the context of risk measures.
Highlights
The employment of nonstandard probability distributions in financial risk theory represents a growing field of research, leading to either theoretical additions as well as relevant practical implications
A relevant role is played by the Skew Normal distributions
Skew Normal distributions are able to capture several aspects of applied science, meaning that they are suitable for a wide range of application, including finance and management science
Summary
The employment of nonstandard probability distributions in financial risk theory represents a growing field of research, leading to either theoretical additions as well as relevant practical implications (see e.g. the monograph [20] and the recent contributions [16, 19]). As far as the multivariate framework is concerned, scanty attention has been paid to an explicit formulation of the expectation of such random variables conditioned to the fact that a prefixed barrier is not ever crossed Such a conditional expectation, known as tail conditional expectation, has been calculated in Bernardi ([8], 2013) for univariate Skew Normal distributions and their mixtures. As recently noted by Bernardi et al ([10], 2017), the TCE= risk measure suffers the lack of the consistency property since it does not preserve the stochastic ordering induced by the bivariate distribution This is especially true for high values of the correlation between variables.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
