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This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry. .

Mathematics. --- Economics, Mathematical. --- Mathematics, general. --- Quantitative Finance. --- Economics --- Mathematical economics --- Math --- Mathematics --- Finance. --- Science --- Funding --- Funds --- Currency question --- Analyse stochastique. --- Mathématiques financières. --- Economics, Mathematical . --- Econometrics --- Methodology

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This book deals with Enterprise Risk Management (ERM) and, in particular, Quantitative Risk Management (QRM) in life insurance business. Constituting a “bridge” between traditional actuarial mathematics and insurance risk management processes, its purpose is to provide advanced undergraduate and graduate students in the Actuarial Sciences, Finance and Economics with the basics of ERM (in general) and QRM applied to life insurance business. The main topics dealt with are: general issues on ERM, risk management tools for life insurance and life annuities, deterministic and stochastic analysis of the behaviour of a portfolio fund, application of sensitivity testing to assess ranges of results of interest, stress testing to assess the impact of extreme scenarios, and the product development process for life annuity products.

Life insurance --- Actuarial science. --- Finance & accounting. --- Risk management. --- Statistics --- Insurance --- Insurance, Life --- Viatical settlements --- Mathematics --- Economics, Mathematical . --- Actuarial Sciences. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Methodology

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This book provides an advanced guide to correlation modelling for credit portfolios, providing both theoretical underpinnings and practical implementation guidance. The book picks up where pre-crisis credit books left off, offering guidance for quants on the latest tools and techniques for credit portfolio modelling in the presence of CVA (Credit Value Adjustments). Written at an advanced level, it assumes that readers are familiar with the fundamentals of credit modelling covered, for example, in the market leading books by Schonbucher (2003) and O'Kane (2008). Coverage will include the latest default correlation approaches; correlation modelling in the 'Marshall-Olkin' contagion framework, in the context of CVA; numerical implementation; and pricing, calibration and risk challenges. The explosive growth of credit derivatives markets in the early-to-mid 000's was bought to a close by the 2007 financial crisis, where these instruments were held largely to blame for the economic downturn. However, in the wake of increased regulation across all financial instruments and the challenge of buying and selling bonds in large amounts, credit derivatives have once again been found to be the answer and the market has grown significantly.Written by a practitioner for practitioners, this book will also interest researchers in mathematical finance who want to understand how things happen and work 'on the floor'. Building the reader's knowledge from the ground up, and with numerous real life examples used throughout, this book will prove a popular reference for anyone with a mathematical mind interested credit markets..

Private finance --- Finance --- Financial organisation --- Marketing --- financieel management --- marketing --- sociale interventies --- financiën --- bankwezen --- Bank marketing. --- Economics, Mathematical. --- Financial Services. --- Quantitative Finance.

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This book provides an analysis, under both discrete-time and continuous-time frameworks, on the price dynamics of leveraged exchange-traded funds (LETFs), with emphasis on the roles of leverage ratio, realized volatility, investment horizon, and tracking errors. This study provides new insights on the risks associated with LETFs. It also leads to the discussion of new risk management concepts, such as admissible leverage ratios and admissible risk horizon, as well as the mathematical and empirical analyses of several trading strategies, including static portfolios, pairs trading, and stop-loss strategies involving ETFs and LETFs. The final part of the book addresses the pricing of options written on LETFs. Since different LETFs are designed to track the same reference index, these funds and their associated options share very similar sources of randomness. The authors provide a no-arbitrage pricing approach that consistently value options on LETFs with different leverage ratios with stochastic volatility and jumps in the reference index. Their results are useful for market making of these options, and for identifying price discrepancies across the LETF options markets. As the market of leveraged exchange-traded products become a sizeable connected part of the financial market, it is crucial to better understand its feedback effect and broader market impact. This is important not only for individual and institutional investors, but also for regulators.

Economic Theory --- Business & Economics --- Exchange traded funds. --- ETFs (Stock funds) --- Stock funds --- Finance. --- Macroeconomics. --- Quantitative Finance. --- Macroeconomics/Monetary Economics//Financial Economics. --- Economics --- Funding --- Funds --- Currency question --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Mathematics --- Methodology

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This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put into the context of generated stochastic processes. Classical mechanics and classical field theory are deterministic processes which emerge when fluctuations in relevant variables are negligible. Quantum mechanics and quantum field theory consider genuine quantum processes. Equilibrium and non-equilibrium statistics apply to the regime where relaxing Markov processes emerge from quantum processes by omission of a large number of uncontrollable variables. Systems with many variables often self-organize in such a way that only a few slow variables can serve as relevant variables. Symmetries and topological classes are essential in identifying such relevant variables. The third aim of this book is to provide conceptually general methods of solutions which can serve as starting points to find relevant variables as to apply best-practice approximation methods. Such methods are available through generating functionals. The potential reader is a graduate student who has heard already a course in quantum theory and equilibrium statistical physics including the mathematics of spectral analysis (eigenvalues, eigenvectors, Fourier and Laplace transformation). The reader should be open for a unifying look on several topics.

Applied Physics --- Engineering & Applied Sciences --- Engineering. --- Finance. --- Theoretical, Mathematical and Computational Physics. --- Engineering, general. --- Quantitative Finance. --- Funding --- Funds --- Economics --- Currency question --- Construction --- Industrial arts --- Technology --- Mathematical physics. --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Mathematics --- Physical mathematics --- Physics --- Methodology