Comment on "Multiple Bosonic Mode Coupling in Electron Self-Energy of (La2−x_{2-x}Srx_x)CuO4_4"

We calculate the photoemission spectral response using the extracted $\alpha^2F$ of Zhou et al (cond-mat/0405130) as an input and we find that the reported Re$\Sigma$ has more strucure than physically possible. Therefore, the "fine structure" most likely reflects the experimental noise.Comment: Comment on cond-mat/0405130, "energy resolution" improve

Structure theorems for certain Gorenstein ideals

The main achievement of this paper is to provide a structure theorem for Artinian, Gorenstein local rings with the property that the square of the maximal ideal is generated by two elements. The moduli problem for this class of local algebras is also discussed. Finally, upper and lower bounds for the minimal number of generators of perfect ideals are given.Comment: 28 page

A family of local rings with rational Poincar\'e Series

In this note we compute the Poincare Series of almost stretched Gorenstein local rings. It turns out that it is rationa

Hilbert Functions of Filtered Modules

In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area of dynamic mathematical activity. Motivated by the ever increasing interest in this field, our goal is to gather together many new developments of this theory into one place, and to present them using a unifying approach which gives self-contained and easier proofs. In this text we shall discuss many results by different authors, following essentially the direction typified by the pioneering work of J. Sally. Our personal view of the subject is most visibly expressed by the presentation of Chapters 1 and 2 in which we discuss the use of the superficial elements and related devices. Basic techniques will be stressed with the aim of reproving recent results by using a more elementary approach. Over the past few years several papers have appeared which extend classical results on the theory of Hilbert functions to the case of filtered modules. The extension of the theory to the case of general filtrations on a module has one more important motivation. Namely, we have interesting applications to the study of graded algebras which are not associated to a filtration, in particular the Fiber cone and the Sally-module. We show here that each of these algebras fits into certain short exact sequences, together with algebras associated to filtrations. Hence one can study the Hilbert function and the depth of these algebras with the aid of the know-how we got in the case of a filtration.Comment: 127 pages, revised version. Comments and remarks are welcom

Financial Market Liquidity and the Lender of Last Resort.

It has been argued in the literature that emergency liquidity injections should be conducted preferably in the form of open market operations. As we show in the present paper, this is not necessarily the case when liquidity may be alternatively used for speculative purposes during the crisis. In such a situation, non-discriminating operations may attract unfunded market participants that divert funding resources away from its best uses in the financial sector. As a consequence, targeted liquidity assistance may become strictly superior. The analysis might have a bearing on recent developments in the context of the subprime crisis.Liquidity ; Financial markets ; Lender of last resort.

Financial market liquidity and the lender of last resort.

In the summer 2007, difficulties in the US subprime mortgage markets have led to disruptive developments in many financial market segments, in particular in interbank money markets, where central banks in the US and in Europe repeatedly intervened to restore smooth market functioning. This article investigates the circumstances in which liquidity shortages may appear in fi nancial markets and evaluates a number of options available to the lender of last resort wishing to restore fi nancial stability. It also suggests that the consideration of balance sheet data is not sufficient for evaluating the risks of leveraged financial entities. Instead, the analysis calls for an explicit consideration of collateral pledges, market illiquidity, and potential non-availability of market prices. Our main messages can be summarised as follows. First, we provide a clear hierarchy across policy alternatives. Taking a risk-efficiency perspective, it turns out that targeted liquidity assistance is preferable to market-wide non-discriminatory liquidity injections. In particular, when liquidity may be alternatively used for speculative purposes during the crisis, non-discriminating open market operations may attract unfunded market participants that divert funding resources away from its best uses in the financial sector. As a consequence, targeted liquidity assistance may become strictly superior. Second, we suggest that forced asset sales may lead to disruptive market developments in a context where financial investors are highly leveraged. Assuming away external funding or renegociability of debt contracts, a fully leveraged investor hit by a liquidity shock would have to liquidate some assets. When markets are not perfectly liquid, asset liquidation depresses market prices. Under standard risk management constraints, lower prices induce a re-evaluation of marked-to-market balance sheets, provoke margin calls, and trigger further selling. In the worst scenario, the leveraged investor may not be able to face the sum of liquidity outfl ows and subsequent margin calls. In that case, the market for illiquid assets breaks down, rendering the valuation of such assets an ambiguous exercise. For investors, such potential trading disruptions imply that the loss that triggers operational default is likely to be much smaller than suggested by standard risk measures.

Forced Portfolio Liquidation.

We study the problem of a leveraged investor that is forced to unwind a significant fraction of its portfolio in a collection of illiquid markets. It is shown that markets may become disrupted in response to a relatively small liquidity shock. As a consequence, the probability of default can be much higher than suggested by standard risk measures. We also study the impact of successful liquidation on relative asset prices. Our analysis suggests that effective risk management of leveraged financial entities should focus on the entity's potential to generate emergency cash-flows net of third-party claims for liquidity.Portfolio liquidation ; Market disruption ; Leverage ; Determinants of asset liquidity ; Hedge funds ; Structured credit.