Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment. Financial Mathematics: A Comprehensive Treatment . (a) Show that the PDF of a sum of two continuous random variables X and Y is given by. Help Center; less. pdf. Financial Mathematics: A Comprehensive Treatment .. The Markov Property and the Transition PDF
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[EPUB] Financial Mathematics: A Comprehensive Treatment by Giuseppe Campolieti, Roman N. Makarov. Book file PDF easily for everyone and every device. Chapman & Hall/CRC FINANCIAL MATHEMATICS SERIES. Financial. Mathematics. A Comprehensive Treatment. Giuseppe Campolieti. Roman N. Makarov. Financial Mathematics: A Comprehensive Treatment provides a unified, self- contained account of the main theory and application of methods.
Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives.
The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance. Or better yet, one for the office and one for the home office.
I commend the authors for their authoritative and comprehensive treatment. The authors treat the subjects rigorously but with plenty of examples, paying close attention to an audience that may encounter the subject matter for the first time, but aware that others will have seen it in different form earlier and may be looking for a different angle.
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Reviews "… brings together under a single cover a comprehensive and descriptive presentation of quantitative finance deftly organized into four major sections … A critically important acquisition for an academic library … especially recommended textbook for undergraduate and graduate students in the fields of mathematics, finance, actuarial science, and economics. Request an e-inspection copy. Share this Title. Related Titles.
Part II is devoted to discrete-time financial modelling. Chapters 5—8 of Part II can be considered as a complete course on discrete-time asset pricing.
Part II introduces the main financial concepts in risk-neutral pricing theory, which are further developed in Part III on continuous-time theory. Chapter 5 covers the financial and formal mathematical un- derpinnings of the single-period Arrow-Debreu economic model.
Chapter 6 lays down the foundation for stochastic processes in discrete time, which is then essential for Chap- ter 7. The latter chapter covers the multi-period binomial market model and is considered the centerpiece of discrete-time financial derivative pricing.
All the important concepts for pricing and hedging standard European, as well as path-dependent derivatives within this model, are presented. A general multi-asset, multi-period, discrete-time model is covered in Chapter 8. This chapter also presents the two fundamental theorems of asset pricing and equivalent martingale measures for discrete-time derivative pricing. Part III is essentially the second half of the textbook and is a major part that is de- voted to continuous-time modelling.
In fact, on its own, Part III i.
Chapter 9 is a stand-alone chapter that sum- marizes the main theoretical concepts in formal probability theory as it relates to measure theory. This also provides some mathematical foundation for later chapters that deal with continuous time modelling and stochastic calculus.
Chapter 10 lays down the foundation for standard Brownian motion. Chapters 12 and 13 are the main chapters on continuous-time derivative pricing theory, which also include the Black-Scholes-Merton theory of European option pricing. The cen- tral concepts of dynamic hedging and replication are presented.
Chapter 12 deals with derivative pricing and hedging in the Black-Scholes-Merton model with a single risky asset. Chapter 12 also covers path-dependent derivative pricing within the Black-Scholes-Merton framework. The chapter combines different techniques for pricing multi-asset financial derivatives.
Var- ious option pricing formulae are then derived.
Chapter 14 is devoted to pricing American options on a single asset. Chapter 15 covers interest-rate modelling and derivative pricing for fixed-income products. Chapter 16 introduces some alternative asset price models, including the local volatility model and solvable state-dependent volatil- ity e.
Part IV concludes the book with Chapters 17 and Chapter 17 is a self-contained exposition of various Monte Carlo and simulation methods that are relevant for simulating financial assets and pricing financial derivatives by simulation. Chapter 18 presents some specific algorithms for the numerical pricing of financial derivatives under various models. The inter-relationship among the different chapters is summarized in the figure, which represents a flow chart of the material in the textbook.
Each solid arrow indicates a strong connection between the material in the respective chapters, i. A dashed arrow indicates that a chapter is relevant but xxvi not necessarily a prerequisite for the other.
Finally, the table below is a reference guide for instructors.