There was a time when scholars were generalists. The great philosophers of ancient Greece were lawyers, theologians, playwrights, political scientists, and naturalists. For instance, Archimedes — BC was a mathematician and engineer, physicist, astronomer, and statesman. In the early Renaissance, Leonardo da Vinci — made significant contributions in art, architecture, music, technology, mathematics, anatomy, geology, botany, physics, and invention.

Isaac Newton — was a physicist, astronomer, mathematician, theologian, and philosopher, while Galileo Galilei — was a technologist, physicist, mathematician, philosopher, and astronomer. As late as the nineteenth century, the mathematician and statistician Carl Friedrich Gauss — was also an astronomer, physicist and geophysicist, theologian, and expert at optics. Oskar Morgenstern and John von Neumann lived at a time when the nascent prevailing formalism in the study of finance had only recently provided an understanding of the meaning of simple financial returns.

Once the financial literature appreciated how returns affected individual decision-making, researchers sought to incorporate risk and uncertainty into their models. Inevitably, this would require significant new work in the understanding of uncertainty and probability, and significantly new complexity in financial models. Before the Great Depression, the simple financial theories of the s had not been put to task. There was little need for nuanced model sophistication to include uncertainty in the ever-rising financial markets of the Roaring Twenties.

By the end of the decade, the markets began to falter. Soon, the economy was plagued with waves of uncertainty that would soon poison financial markets worldwide. The imposition of financial risk on humanity has remained a central topic in finance ever since.

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There became a pressing need to incorporate uncertainty into our understanding of financial markets. The concepts developed in the Theory of Games and Economic Behavior have spawned an incredible literature on strategic behavior in mathematics, economics, finance, political science, sociology, psychology, and many other fields. However, game theory itself has yielded few tools that are of immediate utility in the field of finance.

## The Portfolio Theorists

This is because the implications of game theory are primarily descriptive rather than prescriptive. There have been few great minds that have spawned so many contributions from others as has John von Neumann.

Nor has there likely been a great mind that has imparted so many contributions to so many different scientific fields. Countless scholars have received Nobel Prizes in Physics and Chemistry as a consequence of his pioneering work in a variety of mathematical areas. In the period from the late nineteenth century to the first part of the twentieth century, the classical economic model took center stage, just as the classical model had dominated physics until Albert Einstein shattered its foundations. Calculus was the primary tool for the deterministic models of physics and economics in those days.

However, it depends on well-understood and deterministic relationships using the building blocks of functions that have been used for centuries. The St Petersburg Paradox demonstrated the fundamental incongruency between the measurement of probability and risk, and our human response to it.

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Bernoulli pointed out that humans would not pay an arbitrarily large amount for an infinite return with a probability of less than one. In his hints at how to resolve the Paradox, he noted that it is our subjective human regard for probability that is more relevant than the sterile, rational, mathematic measurement of objective probability. These two great minds began discussions as part of the Second World War research effort while both were researchers at the Columbia University-associated Division for War Research.

It is likely that Leonard Jimmie Savage began to ponder the interdependency of probability and behavior during the year he worked as the statistical analysis assistant to John von Neumann. Both were pure mathematicians who had informed their research based on their extent of human understanding from the emerging economics literature.

When their collaboration ended in , each went in slightly different directions. These new partners bent their once convergent research paths in subtly different directions and finance theory is richer for it. The special case of de Finetti and the more general case of Savage revised how risk and uncertainty affect human decision-making and revolutionized the field of finance. There is a significant debate over whether genius is innate or nurtured.

While it is impossible to determine how our genetic stock might influence the paths we take, we often see genius emerge in consistent ways at young ages. Each of the great minds covered in this series demonstrated flashes, streaks, or consistent and precocious brilliance in their youth. Kenneth J. Arrow, a groundbreaker in finance and almost every other area of the decision sciences, is no exception. In its simplest form, it asked if one would be willing to bet one ducat for the opportunity to flip a coin and possibly win two ducats.

There was a time when scholars were generalists. The great philosophers of ancient Greece were lawyers, theologians, playwrights, political scientists, and naturalists. For instance, Archimedes — BC was a mathematician and engineer, physicist, astronomer, and statesman. In the early Renaissance, Leonardo da Vinci — made significant contributions in art, architecture, music, technology, mathematics, anatomy, geology, botany, physics, and invention.

## The Portfolio Theorists | dequsyjeme.ml

Isaac Newton — was a physicist, astronomer, mathematician, theologian, and philosopher, while Galileo Galilei — was a technologist, physicist, mathematician, philosopher, and astronomer. As late as the nineteenth century, the mathematician and statistician Carl Friedrich Gauss — was also an astronomer, physicist and geophysicist, theologian, and expert at optics. Oskar Morgenstern and John von Neumann lived at a time when the nascent prevailing formalism in the study of finance had only recently provided an understanding of the meaning of simple financial returns.

Once the financial literature appreciated how returns affected individual decision-making, researchers sought to incorporate risk and uncertainty into their models. Inevitably, this would require significant new work in the understanding of uncertainty and probability, and significantly new complexity in financial models. Before the Great Depression, the simple financial theories of the s had not been put to task. There was little need for nuanced model sophistication to include uncertainty in the ever-rising financial markets of the Roaring Twenties.

By the end of the decade, the markets began to falter. Soon, the economy was plagued with waves of uncertainty that would soon poison financial markets worldwide. The imposition of financial risk on humanity has remained a central topic in finance ever since.

There became a pressing need to incorporate uncertainty into our understanding of financial markets. The concepts developed in the Theory of Games and Economic Behavior have spawned an incredible literature on strategic behavior in mathematics, economics, finance, political science, sociology, psychology, and many other fields. However, game theory itself has yielded few tools that are of immediate utility in the field of finance. This is because the implications of game theory are primarily descriptive rather than prescriptive.

There have been few great minds that have spawned so many contributions from others as has John von Neumann. Nor has there likely been a great mind that has imparted so many contributions to so many different scientific fields. Countless scholars have received Nobel Prizes in Physics and Chemistry as a consequence of his pioneering work in a variety of mathematical areas.

In the period from the late nineteenth century to the first part of the twentieth century, the classical economic model took center stage, just as the classical model had dominated physics until Albert Einstein shattered its foundations. Calculus was the primary tool for the deterministic models of physics and economics in those days.

However, it depends on well-understood and deterministic relationships using the building blocks of functions that have been used for centuries. The St Petersburg Paradox demonstrated the fundamental incongruency between the measurement of probability and risk, and our human response to it.

Bernoulli pointed out that humans would not pay an arbitrarily large amount for an infinite return with a probability of less than one.

In his hints at how to resolve the Paradox, he noted that it is our subjective human regard for probability that is more relevant than the sterile, rational, mathematic measurement of objective probability. These two great minds began discussions as part of the Second World War research effort while both were researchers at the Columbia University-associated Division for War Research.

It is likely that Leonard Jimmie Savage began to ponder the interdependency of probability and behavior during the year he worked as the statistical analysis assistant to John von Neumann. Both were pure mathematicians who had informed their research based on their extent of human understanding from the emerging economics literature.

When their collaboration ended in , each went in slightly different directions.

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These new partners bent their once convergent research paths in subtly different directions and finance theory is richer for it. The special case of de Finetti and the more general case of Savage revised how risk and uncertainty affect human decision-making and revolutionized the field of finance. There is a significant debate over whether genius is innate or nurtured.

While it is impossible to determine how our genetic stock might influence the paths we take, we often see genius emerge in consistent ways at young ages. Each of the great minds covered in this series demonstrated flashes, streaks, or consistent and precocious brilliance in their youth. Kenneth J.