סמינרי מחקר היום 4/01/17

In this paper we introduce a novel type of a multivariate tail conditional expectation (MTCE) risk measure and explore its properties. We derive an explicit closed-form expression for this risk measure for the elliptical family of distributions taking into account its variance–covariance dependency structure. Using the MTCE risk measure, we introduce a novel portfolio allocation rule for multivariate loss distributions. As a special case we consider the normal, Student-t and Laplace distributions, important and popular in Actuarial Science and Finance. The motivation behind taking the multivariate TCE for the elliptical family comes from the fact that unlike the traditional tail conditional expectation, the MTCE measure takes into account the covariation between dependent risks, which is the case when we are dealing with real data of losses. We illustrate our results using numerical examples in the case of normal and Student-t distributions.

The episode of the “gatherer of wood ” (מקושש​ עצים) is one of the most enigmatic and troubling stories in the Bible (במדבר טו: לב-לז).  In short, it is puzzling and disturbing that the mere gathering of stic​ks on Shabbat occasioned a public stoning.  Indeed, if an institution can be sustained by love (see Heschel 1951 on the Jewish people’s “love affair” with the Sabbath), why should its “managers” need to sow fear?  I suggest an answer based on (a) recognition of the historical context of the episode-- the “Jewish week” (a seven-day cycle decoupled from natural cycles and peaking with a day of rest) was brand new (Zerubavel 1985); (b) appreciation of the seemingly impossible challenges faced by the would-be “institutional entrepreneur” who might wish to launch the Jewish week in this context; and (c) a close reading of related Biblical texts and especially two other episodes that are intertextually linked with this one— “Pharaoh’s tantrum” (שמות ה) and “the widow of Zarefath” (מלכים א י"ז).  The upshot of the argument is that the wood-gatherer is treated so harshly because he threatens to unleash the “tragedy of the commons” (Hardin 1968; cf., Ostrom 2012), whereby self-interested actors prevent the provision of public goods (in this case, the common stock of fuel).  More generally, the Bible uses this episode to teach us (a) about the collective action problem that is at the heart of the Shabbat (the more people who observe the Shabbat, the stronger are my economic incentives to violate it), especially at its inception; (b) how its institutions—and especially the Shabbat—provide a bulwark against the Hobbesian “war of all against all”; and (c) the grim truth of what “managerial” actions are sometimes necessary to preserve the community