Mortgage Contracts and Underwater Default

We analyze recently proposed mortgage contracts that aim to eliminate selective borrower default when the loan balance exceeds the house price (the ``underwater'' effect). We show contracts that automatically reduce the outstanding balance in the event of house price decline remove the default incentive, but may induce prepayment in low price states. However, low state prepayments vanish if the benefit from home ownership is sufficiently high. We also show that capital gain sharing features, such as prepayment penalties in high house price states, are ineffective as they virtually eliminate prepayment. For observed foreclosure costs, we find that contracts with automatic balance adjustments become preferable to the traditional fixed-rate contracts at mortgage rate spreads between 50-100 basis points. We obtain these results for perpetual versions of the contracts using American options pricing methodology, in a continuous-time model with diffusive home prices. The contracts' values and optimal decision rules are associated with free boundary problems, which admit semi-explicit solutions

A Gaussian Process Approximation for a two-color Randomly Reinforced Urns

We prove a Gaussian process approximation for the sequence of random compositions of a two-color randomly reinforced urn for both the cases with the equal and unequal reinforcement means. By using the Gaussian approximation, the law of the iterated logarithm and the functional limit central limit theorem in both the stable convergence sense and the almost-sure conditional convergence sense are established. Also as a consequence, we are able to to prove that the distribution of the urn composition has no points masses both when the reinforcement means are equal and unequal under the assumption of only finite $(2+\epsilon)$-th moments

Control of the Coupling Strength and the Linewidth of a Cavity-Magnon Polariton

The full coherent control of hybridized systems such as strongly coupled cavity photon-magnon states is a crucial step to enable future information processing technologies. Thus, it is particularly interesting to engineer deliberate control mechanisms such as the full control of the coupling strength as a measure for coherent information exchange. In this work, we employ cavity resonator spectroscopy to demonstrate the complete control of the coupling strength of hybridized cavity photon-magnon states. For this, we use two driving microwave inputs which can be tuned at will. Here, only the first input couples directly to the cavity resonator photons, whilst the second tone exclusively acts as a direct input for the magnons. For these inputs, both the relative phase $\phi$ and amplitude $\delta_0$ can be independently controlled. We demonstrate that for specific quadratures between both tones, we can increase the coupling strength, close the anticrossing gap, and enter a regime of level merging. At the transition, the total amplitude is enhanced by a factor of 1000 and we observe an additional linewidth decrease of $13\%$ at resonance due to level merging. Such control of the coupling, and hence linewidth, open up an avenue to enable or suppress an exchange of information and bridging the gap between quantum information and spintronics applications.Comment: 9 pages, 6 figure

Interaction of hot spots and THz waves in Bi_2Sr_2CaCu_2O_8 intrinsic Josephson junction stacks of various geometry

At high enough input power in stacks of Bi_2Sr_2CaCu_2O8 intrinsic Josephson junctions a hot spot (a region heated to above the superconducting transition temperature) coexists with regions still in the superconducting state. In the ``cold'' regions cavity resonances can occur, synchronizing the ac Josephson currents and giving rise to strong coherent THz emission. We investigate the interplay of hot spots and standing electromagnetic waves by low temperature scanning laser microscopy and THz emission measurements, using stacks of various geometries. For a rectangular and a arrow-shaped structure we show that the standing wave can be turned on and off in various regions of the stack structure, depending on the hot spot position. We also report on standing wave and hot spot formation in a disk shaped mesa structure

Supersymmetric Froggatt-Nielsen Models with Baryon- and Lepton-Number Violation

We systematically investigate the embedding of U(1)_X Froggatt-Nielsen models in (four-dimensional) local supersymmetry. We restrict ourselves to models with a single flavon field. We do not impose a discrete symmetry by hand, e.g. R-parity, baryon-parity or lepton-parity. Thus we determine the order of magnitude of the baryon- and/or lepton violating coupling constants through the Froggatt-Nielsen mechanism. We then scrutinize whether the predicted coupling constants are in accord with weak or GUT scale constraints. Many models turn out to be incompatible.Comment: Final version, references added, minor corrections; LaTeX, 46 page