S -Convex Extrema,Taylor-Type Expansions and Stochastic Approximations

The present work studies s -convex orders using a remarkable probabilistic generalization of Taylor's theorem obtained by Massey & Whitt (1993) and further discussed by Lin (1994). We propose two methods for approximating a given risk with known first moments by means of s -convex extremal distributions. The goodness of those approximations is explored using stop-loss distances. Several applications show the interest of this approach in actuarial sciences.     

Interest rates,government purchases and the Taylor rule in recessions and expansions

In this paper we study asymmetries in the Taylor rule for the United States during the 1970–2012 period. We show that monetary authorities have been constantly concerned with excess demand in overheated periods – when the output gap is positive or the unemployment rate falls below 7% or 7.5% – raising the interest rate aggressively in that case. However, the Fed seems more reluctant to decrease the fund’s rate during recessions. On the contrary, monetary authorities react symmetrically and forcefully to inflation in booms and busts. Finally, we provide evidence that an expansionary fiscal policy does not lead to an increase in interest rates, and thus there is not necessary a “crowding-out” effect in recessions.