On the Mathematics and Economic Assumptions of Continuous-Time Models (Classic Reprint) - Softcover

Inhaltsangabe

Bridge between math and market reality for continuous-time finance

This work explains how elementary probability underpins the mathematical tools used in continuous-time models and the economic assumptions they reflect. It shows why continuous trading is an abstraction, when it can be a good approximation, and how market structure and time scales shape price dynamics and decision making. The book aims to connect theory with real‑world trading and pricing insights.

Readers will see how price changes can be modeled as a sequence of market structures, how martingales arise from unanticipated returns, and how Ito’s calculus provides practical methods for portfolio choice and option pricing. It covers diffusion processes, jump (Poisson) components, and how these elements combine into a flexible framework for analyzing prices and risks in securities markets.

• How continuous-time models relate to discrete trading and why the time scale matters


• Foundations like martingales, Ito’s Lemma, and the separation of diffusion and jump components


• Practical implications for intertemporal portfolios, pricing, and risk assessment


• Guidance on when normality assumptions are convenient and what they actually imply

Ideal for readers of financial economics and quantitative finance seeking a clear, mathematically grounded view of continuous-time models and their economic underpinnings.

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