The generation and reactivity of functionalised organozinc carbenoids for cyclopropane synthesis

This thesis describes the generation and reactivity of functionalised organozinc carbenoids for cyclopropane synthesis with alkenes. In the introductory chapter, a brief overview of the different methods for preparation of heteroatom-functionalised cyclopropanes is presented, including [2+1] cycloaddition reactions using a carbene or carbenoid as a cyclopropanating agent with an alkene, ionic stepwise methods, and chemical modifications from existing cyclopropanes. The remainder of this chapter then focuses on previous work within our own group in this area. The second chapter presents the results obtained from different areas of research in the present study, the first of these being a deeper understanding and extension of the research work undertaken by my predecessor for the development of the cyclopropanation reaction using an “amidoorganozinc” carbenoid derived from N,N diethoxymethyloxazolidinones derivatives in the presence of a source of zinc and chlorotrimethylsilane. Thus, the chemoselectivity and stereoselectivtity of the reaction were fully studied, and a quadrant model was constructed to rationalise the stereochemistry of the products obtained. The second part of this section outlines the generation of new enantiopure organozinc carbenoids precursors derived from substituted chiral precursors followed by the synthesis of novel enantiopure highly functionalised N-cyclopropyl oxazolidinones. The intramolecular version of this cyclopropanation reaction was then successfully studied using diethoxylactam derivatives as organozinc carbenoid precursors. The methodology was then applied to the preparation of novel aminocyclopropyl functionalised compounds selected as interesting building blocks which can lead to the synthesis of natural and biologically active compounds. The fifth part of this chapter describes subsequent studies towards the design of new carbenoid precursors containing additional functional groups of interest. Finally, a brief study on the potential of an organozinc carbenoid to participate in a novel [2,3] sigmatropic rearrangement was investigated. The thesis concludes with a summary of the results obtained, a detailed description of the experimental procedures used and the characterization and analysis of the compounds prepared, together with a full bibliography

A Tale of Two Debt Crises: A Stochastic Optimal Control Analysis

Banks should evaluate whether a borrower is likely to default. I apply several techniques in the extensive mathematical literature of stochastic optimal control/dynamic programming to derive an optimal debt in an environment where there are risks on both the asset and liabilities sides. The vulnerability of the borrowing firm to shocks from either the return to capital, the interest rate or capital gain, increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. As the debt ratio exceeds the optimum, default becomes ever more likely. This paper is “A Tale of Two Crises” because the analysis is applied to the agricultural debt crisis of the 1980s and to the sub-prime mortgage crisis of 2007. A measure of excess debt is derived, and we show that it is an early warning signal of a crisis.optimization, banking, stochastic optimal control, agriculture debt crisis, subprime mortgage crisis

The Diversity of Debt Crises in Europe

The foreign debts of the European countries are at the core of the current crises. Generally, the crises are attributed to government budget deficits in excess of the values stated in the Stability and Growth Pact (SGP)/Maastricht treaty. Proposals for reform generally involve increasing the powers of the European Union to monitor fiscal policies of the national governments and increasing bank regulation. My article is concerned with the following issues. [Q1] How can one explain the inter country differences in the debt crisis in Europe? Is there a single explanation, cause? [Q2] Specifically, were the crises due to government budget deficits or to the private sector? The answer will determine what is the appropriate policy to prevent a recurrence. [Q3] The Stability and Growth Pact/Maastricht Treaty and the European Union focused upon rules concerning government debt ratios and deficit ratios. They ignored the problem of “excessive” debt ratios in the private sector that led to a crisis in the financial markets. Neither the markets nor the Central Banks anticipated the crises until it was too late. My basic questions are: What is an “excessive” private sector debt ratio that is likely to lead to a crisis? What are theoretically based, not empirical ad hoc, Early Warning Signals (EWS) of debt crises? The answers determine to a large extent how one should evaluate proposals for economic reform, to avert future crises?European debt crisis, excess debt, early warning signals, domestic housing sector, government deficit debt

A Critique of the Literature on the US Financial Debt Crisis

A healthy financial system encourages the efficient allocation of capital and risk. The collapse of the house price bubble led to the financial crisis that started in 2007. There is a large empirical literature concerning the relation between asset price bubbles and financial crises. I evaluate the key studies with the respect to the following questions. To what extent do the empirical relations in the existing literature help to identify asset price bubbles ex-ante or ex-post? Do the empirical studies have theoretical foundations? On the basis of that critique, I explain why the application of stochastic optimal control (SOC)/dynamic risk management is a much more effective approach to determine the optimal degree of leverage, the optimum and excessive risk and the probability of a debt crisis. The theoretically founded early warning signals of a crisis are shown to be superior, in general, to those empirical relations in the literature. Moreover the SOC analysis provides a theoretical explanation of the extent that the empirical measures in the literature can be useful.stochastic optimal control, mortgage and financial crises, Ito equation, optimal dynamic risk management, warning signals of crisis, optimal leverage and debt ratios, Congressional Oversight Panel, Case-Shiller index

Application of Stochastic Optimal Control to Financial Market Debt Crises

This interdisciplinary paper explains how mathematical techniques of stochastic optimal control can be applied to the recent subprime mortgage crisis. Why did the financial markets fail to anticipate the recent debt crisis, despite the large literature in mathematical finance concerning optimal portfolio allocation and stopping rules? The uncertainty concerns the capital gain, the return on capital and the interest rate. An optimal debt ratio is derived where the drift is probabilistic but subject to economic constraints. The crises occurred because the market neglected to consider pertinent economic constraints in the dynamic stochastic optimization. The first constraint is that the firm should not be viewed in isolation. The optimizer should be the entire industry. The second economic constraint concerns the modeling of the drift of the price of the asset. The vulnerability of the borrowing firm to shocks from the capital gain, the return to capital or the interest rate, does not depend upon the actual debt/net worth per se. Instead it increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. A general measure of excess debt is derived and I show that it is an early warning signal of the recent crisis.stochastic optimal control, dynamic optimization, mortgage crisis, Ito equation, risk aversion, debt management, warning signals

Stochastic Optimal Control Modeling of Debt Crises

What is an optimal or a sustainable external debt - for a country, region or sector? How should one monitor and evaluate debt to preclude a crisis? We use stochastic optimal control/dynamic programming to derive an optimal debt. The deviation of the actual from the optimal will serve as a Warning Signal of a crisis. There is a correspondence between Hamilton-Jacobi-Bellman equation of Dynamic Programming and the static Mean-Variance (M-V) analysis in finance. A graphic analysis of M-V is helpful to explain the implications of DP. An explicit example is the US Agricultural debt crisis.stochastic optimal control, debt, international finance, US agricultural crisis, Mean-Variance analysis, Hamilton-Jacobi-Bellaman equation

Greenspan, Dodd-Frank and Stochastic Optimal Control

Finanzmarkt; Regulierung; Zentralbank; Kontrolltheorie; USA

Sharing by Design: Data and Decentralized Commons

Ambitious international data-sharing initiatives have existed for years in fields such as genomics, earth science, and astronomy. But to realize the promise of large-scale sharing of scientific data, intellectual property (IP), data privacy, national security, and other legal and policy obstacles must be overcome. While these issues have attracted significant attention in the corporate world, they have been less appreciated in academic and governmental settings, where solving issues of legal interoperability among data pools in different jurisdictions has taken a back seat to addressing technical challenges. Yet failing to account for legal and policy issues at the outset of a large transborder data-sharing project can lead to undue resource expenditures and data-sharing structures that may offer fewer benefits than hoped. We propose a framework to help planners create data-sharing arrangements with a focus on critical early-stage design decisions including options for legal interoperability