UID:
almafu_9959238876102883
Umfang:
1 online resource (vii, 177 pages) :
,
digital, PDF file(s).
ISBN:
1-316-08925-8
,
1-139-56407-2
,
1-283-61080-9
,
1-139-01736-5
,
1-139-55049-7
,
9786613923257
,
1-139-54924-3
,
1-139-55545-6
,
1-139-55420-4
,
1-139-55174-4
Serie:
Mastering mathematical finance
Inhalt:
This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black-Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Itô calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover; Stochastic Calculus for Finance; Series; Title; Copyright; Contents; Preface; 1 Discrete-time processes; 1.1 General definitions; Definition 1.1; Definition 1.5; Definition 1.6; 1.2 Martingales; Definition 1.9; Proposition 1.12; Definition 1.13; Proposition 1.14; Theorem 1.15; Definition 1.16; 1.3 The Doob decomposition; Definition 1.17; Proposition 1.18; Theorem 1.19 Doob decomposition; Proposition 1.20; Proposition 1.21 (Discrete Itô isometry); 1.4 Stopping times; Remark 1.23; Proposition 1.25; Proposition 1.26; Stopped processes; Definition 1.29; Proposition 1.30; Theorem 1.31
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Corollary 1.32Optional sampling for bounded stopping times; Definition 1.33; Proposition 1.34; Theorem 1.35; 1.5 Doob's inequalities and martingale convergence; Theorem 1.36 (Doob's maximal inequality); Theorem 1.37 (Doob's L2-inequality); Lemma 1.38; Theorem 1.39; Theorem 1.40 (Optional sampling); Corollary 1.41; 1.6 Markov processes; The Markov property; Lemma 1.43; Definition 1.44; Definition 1.47; Markov chains; 1.7 Proofs; Lemma 1.38; 2 Wiener process; 2.1 Scaled random walk; Remark 2.1; Proposition 2.2; 2.2 Definition of the Wiener process; Definition 2.4
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2.3 A construction of the Wiener processRemark 2.5; Lemma 2.6; Theorem 2.7; Remark 2.9; 2.4 Elementary properties; Proposition 2.10; Definition 2.11; Definition 2.12; Proposition 2.13; 2.5 Stochastic processes: basic definitions; Definition 2.14; Definition 2.15; Definition 2.16; Definition 2.19; 2.6 Properties of paths; Proposition 2.20; Definition 2.21; Proposition 2.22; Definition 2.23; Proposition 2.24; 2.7 Martingale properties; Definition 2.25; Definition 2.26; Definition 2.27; Proposition 2.28; Definition 2.29; Remark 2.30; Proposition 2.31; Theorem 2.32; Theorem 2.33
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2.8 Doob's inequalitiesLemma 2.34; Proposition 2.35; 2.9 Stopping times; Definition 2.36; Proposition 2.37; Definition 2.38; Definition 2.39; Proposition 2.40; Corollary 2.41; Theorem 2.42 (Optional stopping); Theorem 2.43 (Optional sampling); 2.10 Markov property; Definition 2.44; Proposition 2.45; Definition 2.46; Theorem 2.47; 2.11 Proofs; Theorem 2.7; Theorem 2.43 (Optional Sampling); Lemma 2.48; Lemma 2.49; Lemma 2.50; 3 Stochastic integrals; 3.1 Motivation; 3.2 Definition of the Itô integral; The space M2 of integrands; Proposition 3.2; Definition 3.3; Theorem 3.4
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Integrals of simple processesDefinition 3.5; Remark 3.6; Proposition 3.7 (Linearity); Proposition 3.8; Theorem 3.9; Theorem 3.10; General definition of the integral; Definition 3.11; 3.3 Properties; Theorem 3.13; Theorem 3.14; The stochastic integral as a process; Theorem 3.15; 3.4 It processes; Definition 3.16; Proposition 3.17; Proposition 3.18; Proposition 3.19; Theorem 3.20 (Conditional Itô isometry); Lemma 3.21; Theorem 3.22; Quadratic variation of an It ô process; Lemma 3.23; Theorem 3.24; Theorem 3.25; Theorem 3.26; Theorem 3.27; Remark 3.28; 3.5 Proofs; Theorem 3.4; Lemma 3.29
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Theorem 3.15
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English
Weitere Ausg.:
ISBN 0-521-17573-9
Weitere Ausg.:
ISBN 1-107-00264-8
Sprache:
Englisch
