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Bond Portfolio Optimization
1 The tools of modern portfolio theory are in general use in the equity markets, either in the form of portfolio optimization software or as an accepted frame- 2 work in which the asset managers think about stock selection. In the ?xed income market on the other hand, these tools seem irrelevant or inapplicable. Bond portfolios are nowadays mainly managed by a comparison of portfolio 3 4 risk measures vis ¶a vis a benchmark. The portfolio manager’s views about the future evolution of the term structure of interest rates translate th- selves directly into a positioning relative to his benchmark, taking the risks of these deviations from the benchmark into account only in a very crude 5 fashion, i.e. without really quantifying them probabilistically. This is quite surprising since sophisticated models for the evolution of interest rates are commonly used for interest rate derivatives pricing and the derivation of ?xed 6 income risk measures.
Big Data Science in Finance
Explains the mathematics, theory, and methods of Big Data as applied to finance and investing Examines the mathematics, theory, and practical use of the revolutionary techniques that are transforming the industry. Designed for mathematically-advanced students and discerning financial practitioners alike, this energizing book presents new, cutting-edge content based on world-class research taught in the leading Financial Mathematics and Engineering programs in the world. Marco Avellaneda, a leader in quantitative finance, and quantitative methodology author Irene Aldridge help readers harness the power of Big Data. Provides a complete account of Big Data that includes proofs, step-by-step applications, and code samples Explains the difference between Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) Covers vital topics in the field in a clear, straightforward manner Compares, contrasts, and discusses Big Data and Small Data Includes Cornell University-tested educational materials such as lesson plans, end-of-chapter questions, and downloadable lecture slides
Advanced REIT Portfolio Optimization : Innovative Tools for Risk Management
This book provides an investor-friendly presentation of the premises and applications of the quantitative finance models governing investment in one asset class of publicly traded stocks, specifically real estate investment trusts (REITs). The models provide highly advanced analytics for REIT investment, including: portfolio optimization using both historic and predictive return estimation; model backtesting; a complete spectrum of risk assessment and management tools with an emphasis on early warning systems, risk budgeting, estimating tail risk, and factor analysis; derivative valuation; and incorporating ESG ratings into REIT investment.
Mathematical Control Theory and Finance
This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, ranging from "pure" areas of mathematics up to applied sciences like finance. Stochastic optimal control is a well established and important tool of mathematical finance. Other branches of control theory have found comparatively less applications to financial problems, but the exchange of ideas and methods has intensified in recent years. This volume should contribute to establish bridges between these separate fields. The diversity of topics covered as well as the large array of techniques and ideas brought in to obtain the results make this volume a valuable resource for advanced students and researchers.
Martingale Methods in Financial Modelling
This book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.
Market-Consistent Actuarial Valuation
It is a challenging task to read the balance sheet of an insurance company. This derives from the fact that different positions are often measured by different yardsticks. Assets, for example, are mostly valued at market prices whereas liabilities are often measured by established actuarial methods. Market-Consistent Actuarial Valuation presents powerful methods to measure liabilities and assets in the same way. The mathematical framework that leads to market-consistent values for insurance liabilities is explained in detail by the authors. Topics covered are Stochastic discounting, Valuation portfolio in life and non-life insurance, Asset and liability management, Financial risks, Insurance technical risks, and Solvency.
Malliavin Calculus for Lévy Processes with Applications to Finance
While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated. Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems.
Calcolo stocastico per la finanza = Stochastic Calculation for Finance
Offers an introduction to the mathematical, probabilistic and numerical methods that are the basis of the models for the valuation of derivative instruments, such as options and futures, dealt with in modern financial markets. The book is aimed at readers with scientific training, wishing to develop skills in the field of stochastic calculus applied to finance.
Aspects of Mathematical Finance
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications.
Applied Quantitative Finance
Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance.
Applied Multivariate Statistical Analysis
This book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis.
An Introduction to the Mathematics of Money : Saving and Investing
This is an undergraduate textbook on the basic aspects of personal savings and investing with a balanced mix of mathematical rigor and economic intuition. It uses routine financial calculations as the motivation and basis for tools of elementary real analysis rather than taking the latter as given. Proofs using induction, recurrence relations and proofs by contradiction are covered. Inequalities such as the Arithmetic-Geometric Mean Inequality and the Cauchy-Schwarz Inequality are used. Basic topics in probability and statistics are presented.
Advances in Mathematical Finance
This volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice.
A Course in Credibility Theory and its Applications
It covers the subject of Credibility Theory extensively and includes most aspects of this topic from the simplest case to the most general dynamic model. The first four chapters contain plenty of material The book therefore treats explicitly the tasks which the actuary encounters in his daily work such as estimation of loss ratios, claim frequencies and claim sizes. The models are worked out in detail (including the estimation of structural parameters) so that they can immediately be applied in practice. Most exercises are based on real insurance data and real situations from practice and many of them have the characteristics of a case study. The extension to practical problems arising from the general area of finance is often quite straightforward. This book deserves a place on the bookshelf of every actuary and mathematician who works, teaches or does research in the area of insurance and finance.for a first course on Credibility.
A Benchmark Approach to Quantitative Finance
The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability.
