Ioannis Karatzas Books

Brownian Motion and Stochastic Calculus
Brownian Motion and Stochastic Calculus

By Ioannis Karatzas, Steven Shreve

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This book is designed for a graduate course in stochastic processes. It is written for the reader who is familiar with measure-theoretic probability and the theory of discrete-time processes who is...

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Lectures on the mathematics of finance
Lectures on the mathematics of finance

By Ioannis Karatzas

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In this text, the author discusses the main aspects of mathematical finance. These include arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained...

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If you’ve ever purchased a product online or in a store, you’ve likely come across a barcode. Behind these barcodes lies a standardized system that makes modern commerce possible. Two key codes often encountered are the EAN (European Article Number) and ISBN (International Standard Book Number). But what are they, how are they connected, and why are they so crucial? Let’s explore.

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