Enough Horizon

In this thesis, we develop and analyze a novel framework for moving horizon estimation (MHE) of linear and nonlinear constrained discrete-time systems, which we refer to as proximity moving horizon estimation. The conceptual idea of the proposed framework is to employ a stabilizing a priori solution in order to ensure stability of MHE and to combine it with an online convex optimization in order to obtain an improved performance without jeopardizing stability. The goal of this thesis is to provide proximity-based MHE approaches with desirable theoretical properties and for which reliable and numerically efficient algorithms allow the estimator to be applied in real-time applications. In more detail, we present constructive and simple MHE design procedures which are tailored to the considered class of dynamical systems in order to guarantee important properties of the resulting estimation error dynamics. Furthermore, we develop computationally efficient MHE algorithms in which a suboptimal state estimate is computed at each time instant after an arbitrary and limited number of optimization algorithm iterations. In particular, we introduce a novel class of anytime MHE algorithms which ensure desirable stability and performance properties of the estimator for any number of optimization algorithm iterations, including the case of a single iteration per time instant. In addition to the obtained theoretical results, we discuss the tuning of the performance criteria in proximity MHE given prior knowledge on the system disturbances and illustrate the theoretical properties and practical benefits of the proposed approaches with various numerical examples from the literature.

"Blanche Edith Baughan (1870-1958) was one of New Zealand's first poets and travel writers - her poems were praised for their New Zealand vernacular and her travel writing introduced people here and overseas to our walks and wilderness areas. Born in England, Blanche emigrated to New Zealand in 1900, settling in Sumner and Banks Peninsula, where she embraced the freedom to write and think, and formed friendships with poets Jessie Mackay and Ursula Bethell. It was here that Blanche's interest in the environment and her advocacy for the vulnerable in society flourished. She became a botanist, conservationist and prison reformer, known for her fierce correspondence in defence of her causes"--Back cover.

In 1972, following the huge success of Run Silent, Run Deep, Edward L. Beach's second novel of submarine warfare was published to great acclaim. Like its predecessor, Dust on the Sea was lauded for its authentic portrayal of what it meant to be a submariner during the desperate years of World War II. Tense, dramatic and rich in technical and tactical detail, the book draws on Beach's experience as a submariner in the US Navy to describe the commander and crew of the fictitious USS Eel as they battle overwhelming odds to destroy Japanese ships and save American lives. With no margin for error, the men withstand storms, depth charges and even hand-to-hand combat to defend their boat and themselves. Mistakes, as the title reminds us, result in the debris which serves as a brief grave maker for sunken ships: dust on the sea.

"TAIL RISKS" originate from the failure of mean reversion and the idealized bell curve of asset returns, which assumes that highly probable outcomes occur near the center of the curve and that unlikely occurrences, good and bad, happen rarely, if at all, at either "tail" of the curve. Ever since the global financial crisis, protecting investments against these severe tail events has become a priority for investors and money managers, but it is something Vineer Bhansali and his team at PIMCO have been doing for over a decade. In one of the first comprehensive and rigorous books ever written on tail risk hedging, he lays out a systematic approach to protecting portfolios from, and potentially benefiting from, rare yet severe market outcomes. Tail Risk Hedging is built on the author's practical experience applying macroeconomic forecasting and quantitative modeling techniques across asset markets. Using empirical data and charts, he explains the consequences of diversification failure in tail events and how to manage portfolios when this happens. He provides an easy-to-use, yet rigorous framework for protecting investment portfolios against tail risk and using tail hedging to play offense. Tail Risk Hedging explores how to: Generate profits from volatility and illiquidity during tail-risk events in equity and credit markets Buy attractively priced tail hedges that add value to a portfolio and quantify basis risk Interpret the psychology of investors in option pricing and portfolio construction Customize explicit hedges for retirement investments Hedge risk factors such as duration risk and inflation risk Managing tail risk is today's most significant development in risk management, and this thorough guide helps you access every aspect of it. With the time-tested and mathematically rigorous strategies described here, including pieces of computer code, you get access to insights to help mitigate portfolio losses in significant downturns, create explosive liquidity while unhedged participants are forced to sell, and create more aggressive yet tail-risk-focused portfolios. The book also gives you a unique, higher level view of how tail risk is related to investing in alternatives, and of derivatives such as zerocost collars and variance swaps. Volatility and tail risks are here to stay, and so should your clients' wealth when you use Tail Risk Hedging for managing portfolios. PRAISE FOR TAIL RISK HEDGING: "Managing, mitigating, and even exploiting the risk of bad times are the most important concerns in investments. Bhansali puts tail risk hedging and tail risk management under a microscope--pricing, implementation, and showing how we can fine-tune our risk exposures, which are all crucial ways in how we can better weather our bad times." -- ANDREW ANG, Ann F. Kaplan Professor of Business at Columbia University "This book is critical and accessible reading for fiduciaries, financial consultants and investors interested in both theoretical foundations and practical considerations for how to frame hedging downside risk in portfolios. It is a tremendous resource for anyone involved in asset allocation today." -- CHRISTOPHER C. GECZY, Ph.D., Academic Director, Wharton Wealth Management Initiative and Adj. Associate Professor of Finance, The Wharton School "Bhansali's book demonstrates how tail risk hedging can work, be concretely implemented, and lead to higher returns so that it is possible to have your cake and eat it too! A must read for the savvy investor." -- DIDIER SORNETTE, Professor on the Chair of Entrepreneurial Risks, ETH Zurich

Production is a complex system of interdependent activities, necessary to the system as a whole, which itself depends on the continuance of each individual activity that composes it. In such a system, resources must be committed to specific technological purposes long in advance to the ultimate sale of goods to the consumer.The success of such an enterprise system rests on the durability of the instruments it uses. These are so complex, sensitive, and powerful that their huge expense can be recovered only if they can be used for many years. Yet when the decision is made to invest in them, those years of use are in the future and the conditioning circumstances are unobservable and unknown.The firm in Western economies is the essential institutional means of confronting this problem of uncertainty, Expectation, Enterprise and Profit: The Theory of the Firm is concerned with the nature and mode of life of the firm as a means of policy formation in the face of uncertainty.This book offers a concise treatment and excellent analysis of the major concepts studied in a first course in the theory of the firm.