Essays in Equilibrium Finance

The first chapter, Open-Loop Equilibria and Perfect Competition in Option Exercise Games , a joint work with Professor Kerry Back, is concerned with the optimal exercise and valuation of growth options within a partial equilibrium setting. A finite number of firms invest irreversibly into production capacities. It is well known (see e.g. Dixit and Pindyck (1994)) that irreversibility creates an option-like feature and it is usually not optimal for a monopolistic firm to exercise its investment option when its option is 'at the money'. But what if there is more than one firm competing for market shares? Competing firms invest earlier in equilibrium. With the number of firms going to infinity, the value of the option of waiting to invest approaches zero. In the limit, investment is undertaken as soon as its net present value reaches zero. Our contribution is to provide a rigorous proof for the statement that the strategies in Grenadier (2002) – properly reinterpreted - form an open-loop equilibrium. As open loop strategies lack subgame perfectness, we further show that perfect competition forms a subgame perfect equilibrium already for two firms. In general equilibrium, the central planner's problem is analogous to the monopolistic problem in partial equilibrium. The planner maximizes utility over all admissible investment paths just as a firm maximizes profits. So it is natural to hypothesize that there also exists an 'option premium of waiting to invest' for a welfare maximizing central planner. But how would a delay reconcile with perfect competition and zero profits for firms? This question is addressed in the second chapter within a stylized general equilibrium model with irreversible investment. While it is true that with a single consumption good there are no relative prices within a particular instant of time, i.e. there are no intra-period prices, prices can still be related on their intertemporal dimension. It are precisely the dynamics of intertemporal prices, i.e. interest rates and future prices, that reconcile investment delays with zero profits in the context of the model. Longer term interest rates and futures on wages contain the expected growth-effect of optimally exercised growth options, rendering current investment opportunities unprofitable whenever a delay is efficient. In this sense, the term-structure of future prices reflects the option premium of waiting and leads to optimal delay in investment. Interestingly, this mechanism is similar to what Keynes termed the 'speculative motive' for money demand and liquidity preference. Thinking about Keynes' theory and the speculative motive in particular, naturally leads to questions linked to liquidity preference, such as “What exactly is a liquidity trap? The third and last chapter attempts to make one first step towards this direction by approaching a more elementary question. It asks: Why do people exchange real goods against a piece of paper that neither provides intrinsic utility nor (unlike in Keynes times) constitutes a claim on a real good such as gold? Why is money a safe asset whose value people (can) rely upon? In the model presented in Chapter 3 money is 'safe': Fiat money has strictly positive value in the unique trembling hand equilibrium. This holds as each bank note is both: a witness for the existence of some agent in the economy with debt, backed by collateral, and the only matter that allows the debtor to settle her debt. Debtors fear to lose the collateral and compete with each other for not defaulting. Hence they compete for money. This creates money demand and thereby ensures positive money value. As not only a single but all debtors in the economy demand money, idiosyncratic shocks to solvency wash out. This makes fiat money a safe asset

Case study: The difficulty of correct reference values when evaluating the effects of drought stress: a case study with <i>Thymus vulgaris</i>

Medicinal and spice plants grown under semi-arid conditions frequently contain higher concentrations of relevant secondary metabolites than plants cultivated in moderate regions. It is well established that this phenomenon is due to the impact of drought stress. However, in principle, the increase in natural product concentration could be caused by two quite different effects. Firstly, it could be caused simply by a change of the reference values: typical stress-related reduced growth frequently results in a lower biomass of the stressed plants. In consequence − provided that the rate of natural product biosynthesis remains constant − this results in an enhanced concentration in the stressed plants. Secondly, there is a genuine stress-related increase in the rate of biosynthesis of secondary metabolites. In the first case, the total amount of secondary metabolites remains constant, while in the second case, it increases. Accordingly, a thorough differentiation requires a reliable quantification and comparison of the relevant factors. This especially accounts for the total biomass, which generally is far less in drought stressed plants than in the well-watered ones. Consequently, in all studies, where data on the total biomass are lacking, it is not feasible to evaluate reliably the total amounts of secondary metabolites only on the bases of the concentrations determined. Unfortunately, in most of the corresponding literature published so far, these data are missing, and thus, it is not possible to decide whether the drought stress-related increase of secondary metabolites is due to a genuine increase in biosynthesis or whether it is just due to a change of the relevant reference values, i.e., the total biomass. In this study, the relationships of these factors in well-watered and drought-stressed thyme plants are examined and discussed

Contamination of Plant Foods with Nicotine: An Overview

It is well known that, the explorer "Christopher Columbus" encountered tobacco in the 1400s during his earliest journey to the New World. Tobacco plant is native to North America and other parts of the Western Hemisphere. Furthermore, plant of tobacco contains nicotine and its use has a history that dates back to the earliest records of settlers arriving in America. Moreover, American Indians introduced these settlers to the tobacco plant. In various recent publications elevated nicotine concentrations have been reported to occur in many different foods and plant derived commodities (such as fungi, tea, fruit teas, spices and medicinal plants). Whereas, it is recorded that, high nicotine contaminations are also present in many plant derived products. Up till now, the causes of these contaminations are unknown and they are found in both conventional and in organic products. Thus, field and in vitro experiments are required to elucidate the origin for these nicotine contaminations. Therefore, this work aims to highlight on the nicotine contamination in some different food plants

Barycentric decomposition of quantum measurements in finite dimensions

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k \le d^2 points of the outcome space, d< \infty being the dimension of the Hilbert space. We prove that for second countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points of the outcome space.Comment: !5 pages, no figure

Reexamination of Quantum Bit Commitment: the Possible and the Impossible

Bit commitment protocols whose security is based on the laws of quantum mechanics alone are generally held to be impossible. In this paper we give a strengthened and explicit proof of this result. We extend its scope to a much larger variety of protocols, which may have an arbitrary number of rounds, in which both classical and quantum information is exchanged, and which may include aborts and resets. Moreover, we do not consider the receiver to be bound to a fixed "honest" strategy, so that "anonymous state protocols", which were recently suggested as a possible way to beat the known no-go results are also covered. We show that any concealing protocol allows the sender to find a cheating strategy, which is universal in the sense that it works against any strategy of the receiver. Moreover, if the concealing property holds only approximately, the cheat goes undetected with a high probability, which we explicitly estimate. The proof uses an explicit formalization of general two party protocols, which is applicable to more general situations, and a new estimate about the continuity of the Stinespring dilation of a general quantum channel. The result also provides a natural characterization of protocols that fall outside the standard setting of unlimited available technology, and thus may allow secure bit commitment. We present a new such protocol whose security, perhaps surprisingly, relies on decoherence in the receiver's lab.Comment: v1: 26 pages, 4 eps figures. v2: 31 pages, 5 eps figures; replaced with published version; title changed to comply with puzzling Phys. Rev. regulations; impossibility proof extended to protocols with infinitely many rounds or a continuous communication tree; security proof of decoherence monster protocol expanded; presentation clarifie

Trefoil factor 2 rapidly induces interleukin 33 to promote type 2 immunity during allergic asthma and hookworm infection

The molecular mechanisms that drive mucosal T helper type 2 (T[subscript H]2) responses against parasitic helminths and allergens remain unclear. In this study, we demonstrate in mice that TFF2 (trefoil factor 2), an epithelial cell–derived repair molecule, is needed for the control of lung injury caused by the hookworm parasite Nippostrongylus brasiliensis and for type 2 immunity after infection. TFF2 is also necessary for the rapid production of IL-33, a T[subscript H]2-promoting cytokine, by lung epithelia, alveolar macrophages, and inflammatory dendritic cells in infected mice. TFF2 also increases the severity of allergic lung disease caused by house dust mite antigens or IL-13. Moreover, TFF2 messenger RNA expression is significantly increased in nasal mucosal brushings during asthma exacerbations in children. These experiments extend the biological functions of TFF2 from tissue repair to the initiation and maintenance of mucosal T[subscript H]2 responses

Expression of SARS-CoV-2 Entry Factors in the Pancreas of Normal Organ Donors and Individuals with COVID-19

This article is made available for unrestricted research re-use and secondary analysis in any form or be any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Diabetes is associated with increased mortality from severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). Given literature suggesting a potential association between SARS-CoV-2 infection and diabetes induction, we examined pancreatic expression of angiotensin-converting enzyme 2 (ACE2), the key entry factor for SARS-CoV-2 infection. Specifically, we analyzed five public scRNA-seq pancreas datasets and performed fluorescence in situ hybridization, western blotting, and immunolocalization for ACE2 with extensive reagent validation on normal human pancreatic tissues across the lifespan, as well as those from coronavirus disease 2019 (COVID-19) cases. These in silico and ex vivo analyses demonstrated prominent expression of ACE2 in pancreatic ductal epithelium and microvasculature, but we found rare endocrine cell expression at the mRNA level. Pancreata from individuals with COVID-19 demonstrated multiple thrombotic lesions with SARS-CoV-2 nucleocapsid protein expression that was primarily limited to ducts. These results suggest SARS-CoV-2 infection of pancreatic endocrine cells, via ACE2, is an unlikely central pathogenic feature of COVID-19-related diabetes.We thank the families of the organ donors and autopsy subjects for the gift of tissues. We also thank Jill K. Gregory, CMI (Icahn School of Medicine at Mount Sinai, New York, NY) for preparing the graphical abstract. These efforts were supported by NIH P01 AI042288 and UC4 DK108132 (M.A.A.); JDRF (M.A.A.); NIH R01 DK122160 (M.C.-T.); NIH R01 AI134971 and P30 DK020541 (D.H.); JDRF 3-PDF-2018-575-A-N (V.V.D.H.); R01 DK093954 , R21 DK119800-01A1 , UC4 DK104166 , and U01 DK127786 (C.E.-M.); VA Merit Award I01BX001733 (C.E.-M.); Imaging Core of NIH/ NIDDK P30 DK097512 (C.E.-M.); gifts from the Sigma Beta Sorority , the Ball Brothers Foundation , and the George and Frances Ball Foundation (C.E.-M.); the Network for Pancreatic Organ Donors with Diabetes ( nPOD ; RRID: SCR_014641 ) ( 5-SRA-2018-557-Q-R ); and The Leona M. & Harry B. Helmsley Charitable Trust ( 2018PG-T1D053 ). The authors also wish to acknowledge the Islet and Physiology Core of the Indiana Diabetes Research Center ( P30DK097512 ). The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication