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Foundations of Quantitative Finance
This advanced ten-volume series is logically sequential. Books I, III, and V develop foundational mathematics needed for the probability theory and finance applications of Books II, IV, and VI, respectively. Books VII, VIII, and IX then develop results on stochastic processes used in finance, with the final development of applications of these models to finance deferred to Book X.
The target audience includes graduate students, advanced practitioners, and researchers in finance who are quantitatively literate, and seek the detailed developments of the materials presented.
All ten volumes are extensively self-referenced. The reader can enter the collection at any point of interest, and then using the references cited, work backwards to prior books to fill in needed details.
Foundations of Quantitative Finance Book I: Measure Spaces and Measurable Functions
Foundations of Quantitative Finance Book II: Probability Spaces and Random Variables
Foundations of Quantitative Finance Book III: The Integrals of Lebesgue and (Riemann-)Stieltjes
Foundations of Quantitative Finance Book IV: Distribution Functions and Expectations
Foundations of Quantitative Finance Book V: General Measure and Integration Theory
Foundations of Quantitative Finance Book VI: Densities, Transformed Distributions and Limit Theorems
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Foundations of Quantitative Finance Book VII: Brownian Motion and Other Stochastic Processes
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Foundations of Quantitative Finance Book VIII: Itô Integration and Stochastic Calculus 1
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Foundations of Quantitative Finance Book IX: Stochastic Calculus 2 and Stochastic Differential Equations
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