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# đź“™ Stochastic Finance: An Introduction in Discrete Time by Hans FĂ¶llmer, Alexander Schied â€” download pdf

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This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry.

The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage.

The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk.

In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk.

This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures.

**Contents: Part I: Mathematical finance in one period**

Arbitrage theory

Preferences

Optimality and equilibrium

Monetary measures of risk

Dynamic arbitrage theory

American contingent claims

Superhedging

Efficient hedging

Hedging under constraints

Minimizing the hedging error

Dynamic risk measures

- Series:
**de Gruyter Textbook** - Author:
**Hans FĂ¶llmer, Alexander Schied** - Year:
**2016** - Publisher:
**de Gruyter** - Language:
**English** - ISBN:
**311046344X,9783110463446**

- File size:
**2 981 400** - Format:
**pdf**

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This book is an introduction to financial mathematics for mathematicians. It is intended both for graduate students with a certain background in probability theory as well as for professional mathematicians in industry and academia. In contrast to many te...

This is the third, revised and extended edition of the classical introduction to the mathematics of finance, based on stochastic models in discrete time. In the first part of the book simple one-period models are studied, in the second part the idea of dy...

This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry.The focus on stochastic models in discrete time has two immediate benefits. First, the probabil...

Intended for graduate students in mathematics, this textbook is an introduction to probabilistic methods in finance that focuses on stochastic models in real time. It is based on courses taught by the authors at Humboldt U. and Technical U. in Germany. Th...

Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, ...

INTRODUCTION DISCRETE-TIME MODELS Discrete-time formalismMartingales and arbitrage opportunities Complete markets and option pricing Problem: Cox, Ross and Rubinstein model OPTIMAL STOPPING PROBLEM AND AMERICAN OPTIONS Stopping time The Snell envelope Dec...

In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real proces...

This book provides a comprehensive introduction to stochastic control problems in discrete and continuous time. The material is presented logically, beginning with the discrete-time case before proceeding to the stochastic continuous-time models. Central ...

In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real proces...