Leverage Bubbles

This paper investigates the relation between liquidity and asset prices. It shows that, when banks balance sheets are marked to market and banks are targeting a financial leverage level - a situation similar to current environment - formation of Leverage Bubble phenomenon and suggests a new regulation rule based on a Dynamic Leverage Ratio (DLR) rule.Financial crises, rational bubbles, Dynamic Leverage Ratio, mark to market accounting, asset pricing, macroprudential regulation, market liquidity.

Monetary Policy with Incomplete Markets

We consider an extension of a general equilibrium model with incomplete markets that considers cash-in-advance constraints. The total amount of money is supplied by an authority, which produces at no cost and lends money to agents at short term nominal rates of interest, meeting the demand. Agents have initial nominal claims, which in the aggregate, are the counterpart of an initial public debt. The authority covers its expenditures, including initial debt, through public revenues which consists of taxes and seignorage, and distributes its eventual budget surpluses through transfers to individuals, while no further instruments are available to correct eventual budget deficits. We define a concept of equilibrium in this extended model, and prove that there exists a monetary equilibrium with no transfers. Moreover, we show that if the price level is high enough, a monetary equilibrium with positive transfers exists.Cash-in-advance constraints, incomplete markets, nominal assets, monetary equilibrium, money, nominal interest rate, transfers, price levels

New Stability Estimates for the Inverse Medium Problem with Internal Data

A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly determined from the data itself. To our knowledge, in the most existing stability results, the boundary conditions are assumed to be close to a set of CGO solutions where the critical points can be avoided. We establish in the present work new weighted stability estimates for an electro-acoustic inverse problem without assumptions on the presence of critical points. These results show that the Lipschitz stability far from the critical points deteriorates near these points to a logarithmic stability

Stability estimates for the fault inverse problem

We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on the boundary of the half space. Displacement fields present jumps across faults, called slips, while traction derivatives are continuous. It was proved in \cite{volkov2017reconstruction} that if the displacement field is known on an open set on the boundary of the half space, then the fault and the slip are uniquely determined. In this present paper, we study the stability of this uniqueness result with regard to the coefficients of the equation of the plane containing the fault. If the slip field is known we state and prove a Lipschitz stability result. In the more interesting case where the slip field is unknown, we state and prove another Lipschitz stability result under the additional assumption, which is still physically relevant, that the slip field is one directional

H\"older Stability for an Inverse Medium Problem with Internal Data

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We precisely show that we have actually a stability estimate of H\"older type. For sake of simplicity, we limited our study to the class of Helmholtz equations $\Delta$+V with bounded potential V