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Methods of Mathematical Finance (Stochastic Modelling and Applied Probability)

Methods of Mathematical Finance

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87,598 ratings · 4,993 reviews
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Methods of Mathematical Finance (Stochastic Modelling and Applied Probability)

Methods of Mathematical Finance

4.85 87,598 ratings · 4,993 reviews
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Overview: This monograph is a sequel to 'Brownian Motion and Stochastic Calculus' by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes decribing the field, including topics not treated in the text.This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

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Published September 21, 1998
ISBN 534343
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After spending years working in the corporate world, Ioannis Karatzas finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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William Scott
William Scott February 21, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
James Hill
James Hill August 20, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Sharon Roberts June 11, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Michael Young May 18, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Mary Rivera October 06, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Mary Rivera February 20, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Kenneth Perez February 01, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
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Betty Baker April 18, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Michael Green
Michael Green June 01, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Barbara Johnson
Barbara Johnson March 05, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
James Green
James Green March 14, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Charles Hill
Charles Hill September 10, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
George Rivera
George Rivera August 22, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Nancy Moore March 30, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Betty Scott
Betty Scott February 13, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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William Scott November 29, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
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A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Rebecca Robinson
Rebecca Robinson October 13, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Ashley Hill
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Patricia Evans April 03, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
James Evans
James Evans April 15, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Amanda Baker
Amanda Baker May 01, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Dorothy  Parker
Dorothy Parker May 03, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Daniel Gonzalez
Daniel Gonzalez January 07, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Paul Wilson
Paul Wilson January 09, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Robert Williams
Robert Williams June 07, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Brian Ramirez
Brian Ramirez January 26, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Jessica Cruz
Jessica Cruz November 26, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Cynthia Green May 17, 2024
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
Richard Anderson
Richard Anderson October 24, 2024
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Sharon Rodriguez
Sharon Rodriguez February 13, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Charles Williams September 02, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Jacob Brown March 27, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Patricia Sanchez
Patricia Sanchez April 13, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Kevin Jackson
Kevin Jackson February 06, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Margaret Walker
Margaret Walker June 11, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Rebecca Robinson
Rebecca Robinson February 25, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Sandra Moore
Sandra Moore January 23, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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Sandra Diaz January 09, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Carol Hernandez
Carol Hernandez June 18, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Jennifer Anderson
Jennifer Anderson December 27, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Dorothy Evans
Dorothy Evans September 28, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Donald Gomez
Donald Gomez March 26, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Mark Brown
Mark Brown November 30, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Rebecca Johnson
Rebecca Johnson June 19, 2024
A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
Andrew Lopez
Andrew Lopez February 10, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Sharon Nelson
Sharon Nelson June 18, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Sandra Diaz
Sandra Diaz December 29, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Sharon Nelson
Sharon Nelson March 28, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Donald Anderson
Donald Anderson January 20, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Laura Hill
Laura Hill November 22, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Ryan Lopez
Ryan Lopez April 06, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Donald Smith
Donald Smith November 04, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Amanda Allen
Amanda Allen May 22, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Mary Rodriguez
Mary Rodriguez May 22, 2024
Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Christopher Wright
Christopher Wright October 09, 2024
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
Charles Martin
Charles Martin October 06, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
William Reyes
William Reyes February 19, 2024
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Charles Edwards
Charles Edwards December 03, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Gary Lewis
Gary Lewis October 17, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
George Harris
George Harris December 13, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Mary Torres
Mary Torres August 01, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Richard Harris
Richard Harris February 15, 2025
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average.
Robert Robinson
Robert Robinson January 18, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Kenneth Perez
Kenneth Perez July 05, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Barbara Wilson
Barbara Wilson May 11, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Richard Lopez
Richard Lopez January 14, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Steven Walker
Steven Walker August 12, 2025
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Jennifer Martin
Jennifer Martin September 28, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Steven  Parker
Steven Parker November 25, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
John Moore
John Moore April 24, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Mary Baker
Mary Baker August 01, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Joseph Lee
Joseph Lee July 26, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Brian Ramirez
Brian Ramirez March 22, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Kimberly Taylor
Kimberly Taylor February 05, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Donna Perez
Donna Perez April 10, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Linda Lewis
Linda Lewis December 10, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
James Robinson
James Robinson May 02, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
John Hernandez
John Hernandez August 29, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Richard Turner
Richard Turner July 19, 2025
It was adequate. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
Stephanie Gonzalez
Stephanie Gonzalez September 08, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Jessica Roberts
Jessica Roberts February 02, 2024
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Michael Hill
Michael Hill July 01, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Amanda Turner
Amanda Turner June 26, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Matthew Green
Matthew Green October 06, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Charles Hernandez
Charles Hernandez April 15, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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