INTERFERENCE OF CLOSABLE CRACKS AND NARROW SLITS IN AN ELASTIC PLATE UNDER BENDING

The problem of bending of an infinite plate containing an array of trough closable cracks and narrow slits is considered in a two-dimensional statement. A crack is treated as a mathematical cut, the edges of which are able to contact along the line on the plate outside. A slit is referred to as a cut with contact stress-free surfaces and the negative jump of normal displacement can occur on this cut. The crack closure caused by bending deformation was studied based on the classical hypothesis of direct normal and previously developed model of the contact of edges along the line. A new boundary problem for a couple of biharmonic equations of plane stress and plate bending with interconnected boundary conditions in the form of inequalities on the cuts is formulated. The method of singular integral equations was applied in order to develop approximate analytical and numerical solutions to the problem. The forces and moments intensity factors near the peaks of defects and contact reaction on the closed edges of the cracks are calculated. A detailed analysis was carried out for parallel rectilinear crack and slit, depending on their relative location. Presented results demonstrate qualitative differences in the stress concentration near the defects of different nature.

The Term Structures of Expected Loss and Gain Uncertainty*

We document that the term structures of risk-neutral expected loss and gain uncertainty on S&P 500 returns are upward sloping on average. These shapes mainly reflect the higher premium required by investors to hedge downside risk and the belief that potential gains will increase in the long run. The term structures exhibit substantial time-series variation with large negative slopes during crisis periods. Through the lens of a flexible Jump-Diffusion framework, we evaluate the ability of existing reduced-form option pricing models to replicate these term structures. We stress that three ingredients are particularly important: (i) the inclusion of jumps; (ii) disentangling the price of negative jump risk from its positive analog in the stochastic discount factor specification; and (iii) specifying three latent factors.

BORDER COLLISION BIFURCATIONS IN 1D PWL MAP WITH ONE DISCONTINUITY AND NEGATIVE JUMP: USE OF THE FIRST RETURN MAP

The aim of this work is to study discontinuous one-dimensional maps in the case of slopes and offsets having opposite signs. Such models represent the dynamics of applied systems in several disciplines. We analyze in particular attracting cycles, their border collision bifurcations and the properties of the periodicity regions in the parameter space. The peculiarity of this family is that we can make use of the technical instrument of the first return map. With this, we can rigorously prove properties which were known numerically, as well as prove new ones, giving a complete characterization of the overlapping periodicity regions.