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Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations, in financial data, stock-market shocks, risk management, ...) play an increasingly important role. This much awaited book presents a comprehensive development of extreme value methodology for random walk models, time series, certain types of continuous-time stochastic processes and compound Poisson processes, all models which standardly occur in applications in insurance mathematics and mathematical finance. Both probabilistic and statistical methods are discussed in detail, with such topics as ruin theory for large claim models, fluctuation theory of sums and extremes of iid sequences, extremes in time series models, point process methods, statistical estimation of tail probabilities. Besides summarising and bringing together known results, the book also features topics that appear for the first time in textbook form, including the theory of subexponential distributions and the spectral theory of heavy-tailed time series. A typical chapter will introduce the new methodology in a rather intuitive (tough always mathematically correct) way, stressing the understanding of new techniques rather than following the usual "theorem-proof" format. Many examples, mainly from applications in insurance and finance, help to convey the usefulness of the new material. A final chapter on more extensive applications and/or related fields broadens the scope further. The book can serve either as a text for a graduate course on stochastics, insurance or mathematical finance, or as a basic reference source. Its reference quality is enhanced by a very extensive bibliography, annotated by various comments sections making the book broadly and easily accessible.

Actuarial science. --- Business mathematics. --- Econometrics. --- Economics, Mathematical . --- Probabilities. --- Finance. --- Actuarial Sciences. --- Business Mathematics. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Finance, general.

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A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems such as portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed.

Capital market --- Convergence. --- Stochastic processes. --- Mathematical models. --- AA / International- internationaal --- 305.91 --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Convergence --- Stochastic processes --- Random processes --- Probabilities --- Functions --- Mathematical models --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Public finance. --- Finance. --- Economics, Mathematical . --- Public Economics. --- Finance, general. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Funding --- Funds --- Currency question --- Cameralistics --- Public finance --- Public finances --- Methodology

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Continuous-time finance was developed in the late sixties and early seventies by R. C. Merton. Over the years, due to its elegance and analytical conve­ nience, the continuous-time paradigm has become the standard tool of anal­ ysis in portfolio theory and asset pricing. However, and probably because it was developed hand in hand with option pricing, in which investors' expecta­ tions were thought not to matter, continuous-time finance has for a long time almost entirely neglected investors' beliefs. More recently, the development of martingale pricing techniques, in which expectations playa dominant role, and the blurring boundary between those methods and the original methods of continuous-time finance based on the Ito calculus, have allowed expecta­ tions to regain their central role in finance. The habilitation thesis of Professor Alexandre Ziegler is entirely devoted to the role of expectations in continuous-time finance. After a brief review of the literature, the author analyzes the consequences of incomplete informa­ tion and heterogeneous beliefs for optimal portfolio and consumption choice and equilibrium asset pricing. Relaxing the assumption that investors can ob­ serve expected dividend growth perfectly, the author shows that incomplete information affects stock prices and their dynamics, thus providing a potential explanation for the asset price bubble of the late 1990s. He also demonstrates how the presence of heterogeneous beliefs among investors affects their opti­ mal portfolios and their optimal consumption patterns.

Options (Finance) --- Options (Finances) --- Prices --- Mathematical models. --- Prix --- Modèles mathématiques --- AA / International- internationaal --- 305.91 --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Modèles mathématiques --- Call options --- Calls (Finance) --- Listed options --- Options exchange --- Options market --- Options trading --- Put and call transactions --- Put options --- Puts (Finance) --- Prices&delete& --- Mathematical models --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Derivative securities --- Investments --- Finance. --- Economics, Mathematical . --- Finance, general. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Funding --- Funds --- Currency question --- Methodology

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Financial Markets Theory presents classical asset pricing theory, a theory composed of milestones such as portfolio selection, risk aversion, fundamental asset pricing theorem, portfolio frontier, CAPM, CCAPM, APT, the Modigliani-Miller Theorem, no arbitrage/risk neutral evaluation and information in financial markets. Starting from an analysis of the empirical tests of the above theories, the author provides a discussion of the most recent literature, pointing out the main advancements within classical asset pricing theory and the new approaches designed to address open problems (e.g. behavioural finance). It is the only textbook to address the economic foundations of financial markets theory from a mathematically rigorous standpoint, and to offer a self-contained critical discussion, based on empirical results. Financial Markets Theory is an advanced book, well-suited for a first graduate course in financial markets, economics or financial mathematics. It is self-contained and introduces topics in a setting accessible to economists and practitioners equipped with a basic mathematical background. For those not acquainted with standard microeconomic theory, the tools needed to follow the analysis are presented early in the book. The approach makes this a vital handbook for practitioners in insurance, banking, investment funds and financial consultancy, as well as an excellent graduate-reference textbook.

Capital market --- Equilibrium (Economics) --- Marché financier --- Equilibre (Economie politique) --- Mathematical models. --- Modèles mathématiques --- AA / International- internationaal --- 305.7 --- 333.600 --- -Equilibrium (Economics) --- -332.0410151 --- Capital markets --- Market, Capital --- Finance --- Financial institutions --- Loans --- Money market --- Securities --- Crowding out (Economics) --- Efficient market theory --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente. --- Financiële markten. Kapitaalmarkten (algemeenheden). --- Mathematical models --- Marché financier --- Modèles mathématiques --- 332.0410151 --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente --- Financiële markten. Kapitaalmarkten (algemeenheden) --- Economic theory. --- Public finance. --- Economics, Mathematical . --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Public Economics. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Cameralistics --- Public finance --- Public finances --- Currency question --- Economic theory --- Political economy --- Social sciences --- Economic man --- Methodology

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Mathematical statistics --- 519.2 --- 330.115 --- Finance --- -Time-series analysis --- -AA / International- internationaal --- 305.91 --- 305.7 --- 304.0 --- 303.0 --- -332.0151955 --- Funding --- Funds --- Economics --- Currency question --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Probabilities --- Probability. Mathematical statistics --- Econometrie --- Mathematical models --- Econometric models --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente. --- Zuivere statistische analyse (algemene naslagwerken). Tijdreeksen. --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken). --- S-Plus. --- SPlus --- 330.115 Econometrie --- 519.2 Probability. Mathematical statistics --- Econometrics. --- Computer software. --- Programming languages (Electronic computers). --- Statistics . --- Economics, Mathematical . --- Mathematical Software. --- Programming Languages, Compilers, Interpreters. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Quantitative Finance. --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Electronic data processing --- Languages, Artificial --- Software, Computer --- Computer systems --- Economics, Mathematical --- Statistics --- Mathematical economics --- Econometrics --- Mathematics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Methodology --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente --- Zuivere statistische analyse (algemene naslagwerken). Tijdreeksen --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken) --- -Finance --- -Mathematical models