This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

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Quantitative Risk Management: Concepts, Techniques, and Tools

List of notations Preface to the second edition Preface to the first edition 1. Stochastic programming models 2. Two-stage problems 3. Multistage problems 4. Optimization models with probabilistic constraints 5. Statistical inference 6. Risk averse optimization 7. Background material 8. Bibliographical remarks Bibliography Index.

Lectures on Stochastic Programming: Modeling and Theory

We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b).

Backward Stochastic Differential Equations in Finance

A general version of the fundamental theorem of asset pricing.

Non-Gaussian processes of Ornstein–Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive OU processes, and we study these models in relation to financial data and theory.

Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics

We solve the problems of mean–variance hedging (MVH) and mean–variance portfolio selection (MVPS) under restricted information. We work in a setting where the underlying price process S is a semima...

Dynamic mean–variance optimization problems with deterministic information

Let $X$ be a semimartingale and $\Theta$ the space of all predictable $X$-integrable processes $\vartheta$ such that $\int\vartheta dX$ is in the space $\mathscr{S}^2$ of semimartingales. We consider the problem of approximating a given random variable $H \in\mathscr{L}^2$ by a stochastic integral $\int^T_0 \vartheta_s dX_s$, with respect to the $\mathscr{L}^2$-norm. If $X$ is special and has the form $X = X_0 + M + \int \alpha d\langle M\rangle$, we construct a solution in feedback form under the assumptions that $\int \alpha^2 d\langle M\rangle$ is deterministic and that $H$ admits a strong F-S decomposition into a constant, a stochastic integral of $X$ and a martingale part orthogonal to $M$. We provide sufficient conditions for the existence of such a decomposition, and we give several applications to quadratic optimization problems arising in financial mathematics.

Approximating Random Variables by Stochastic Integrals

We provide three characterizations of the minimal martingale measure P associated to a given d- dimensional semimartingale X. In each case, P is shown to be the unique solution of an optimization problem where one minimizes a certain functional over a suitable class of signed local martingale measures for X. Furthermore, we extend a result of Ansel and Stricker on the Foellmer-Schweizer decomposition to the case where X is continuous, but multidimensional.

On the Minimal Martingale Measure and the Foellmer- Schweizer Decomposition

https://people.math.ethz.ch/~mschweiz/Files/RSS-final.pdf

Martin Schweizer

Papers

Dynamic mean–variance optimization problems with deterministic information

Approximating Random Variables by Stochastic Integrals

On the Minimal Martingale Measure and the Foellmer- Schweizer Decomposition

From structural assumptions to a link between assets and interest rates

Weighted Norm Inequalities and Hedging in Incomplete Markets