Introductory mathematical analysis for quantitative finance

by Ritelli, Daniele

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Title Statements

Full title :Introductory mathematical analysis for quantitative finance

Summary

Introductory Mathematical Analysis for Quantitative Finance is a textbook designed to enable students with little knowledge of mathematical analysis to fully engage with modern quantitative finance. A basic understanding of dimensional Calculus and Linear Algebra is assumed. The exposition of the topics is as concise as possible, since the chapters are intended to represent a preliminary contact with the mathematical concepts used in Quantitative Finance. The aim is that this book can be used as a basis for an intensive one-semester course. Features: • Written with applications in mind, and maintaining mathematical rigor. • Suitable for undergraduate or master's level students with an Economics or Management background. • Complemented with various solved examples and exercises, to support the understanding of the subject.

Edition Statements

Publication Date:2020

Publication Statements

Publisher(s):CRC Press-Chapman & Hall
Place of Publication:Boca Raton, FL
Language:eng
Publication Date:2020

The Physical Object

Description:303 s.

Edition Identifiers

ISBN:9780815372547, 081537254X
oclc:on1230247086

1 Euclidean space: 1.1 Vectors -- 1.2 Topology of ℝn -- 1.3 Limits of functions -- 2 Sequences and series of functions: 2.1 Sequences and series of real or complex numbers -- 2.2 Sequences of functions -- 2.3 Uniform convergence -- 2.4 Series of functions -- 2.5 Power series: radius of convergence -- 2.6 Taylor-Maclaurin series -- 2.6.1 Binomial series -- 2.6.2 The error function -- 2.6.3 Abel theorem and series summation -- 2.7 Basel problem -- 2.8 Extension of elementary functions to the complex field -- 2.8.1 Complex exponential -- 2.8.2 Complex goniometric hyperbolic functions -- 2.8.3 Complex logarithm -- 2.9 Exercises -- 2.9.1 Solved exercises -- 2.9.2 Unsolved exercises -- 3 Multidimensional differential calculus: 3.1 Partial derivatives -- 3.2 Differentiability -- 3.3 Maxima and Minima -- 3.4 Sufficient conditions -- 3.5 Lagrange multipliers -- 3.6 Mean-Value theorem -- 3.7 Implicit function theorem -- 3.8 Proof of Theorem 3.22 -- 3.9 Sufficient conditions -- 4 Ordinary differential equations of first order: general theory: 4.1 Preliminary notions -- 4.1.1 Systems of ODEs: equations of high order -- 4.2 Existence of solutions: Peano theorem -- 4.3 Existence and uniqueness:…