Shoutir Kishore Chatterjee
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198525318
- eISBN:
- 9780191711657
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525318.003.0006
- Subject:
- Mathematics, Probability / Statistics
After James Bernoulli, the main contributors to probability theory and its applications in the 18th century worked either to solve more intricate problems of games of chance (De Moivre), or to build ...
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After James Bernoulli, the main contributors to probability theory and its applications in the 18th century worked either to solve more intricate problems of games of chance (De Moivre), or to build new probability models (De Moivre, Daniel Bernoulli). Further, some of them used probabilistic arguments to test hypotheses about or to estimate parameters involved in probability models for real life phenomena in the fields of demography, astronomy, and theory of errors. The concept of continuous variables, the tool of generating functions, the normal model approximation to the binomial, and ‘the rational expectation principle’ (in the context of the St. Petersburg Paradox) emerged out of these studies.Less
After James Bernoulli, the main contributors to probability theory and its applications in the 18th century worked either to solve more intricate problems of games of chance (De Moivre), or to build new probability models (De Moivre, Daniel Bernoulli). Further, some of them used probabilistic arguments to test hypotheses about or to estimate parameters involved in probability models for real life phenomena in the fields of demography, astronomy, and theory of errors. The concept of continuous variables, the tool of generating functions, the normal model approximation to the binomial, and ‘the rational expectation principle’ (in the context of the St. Petersburg Paradox) emerged out of these studies.
Eric Barthalon
- Published in print:
- 2014
- Published Online:
- November 2015
- ISBN:
- 9780231166287
- eISBN:
- 9780231538305
- Item type:
- chapter
- Publisher:
- Columbia University Press
- DOI:
- 10.7312/columbia/9780231166287.003.0010
- Subject:
- Economics and Finance, Behavioural Economics
This chapter focuses on the psychological importance of downside risk by presenting Maurice Allais's paradox and by contrasting how Allais and prospect theory have interpreted this paradox. It also ...
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This chapter focuses on the psychological importance of downside risk by presenting Maurice Allais's paradox and by contrasting how Allais and prospect theory have interpreted this paradox. It also considers whether the HRL formulation can be used to model how financial market participants form “expectations” of the dispersion of returns under uncertainty. The chapter begins with a brief overview of expected utility theory, with particular emphasis on the Saint Petersburg paradox and how it was resolved by Daniel Bernoulli in 1738. It then considers the Allais paradox and its conflicting interpretations, including prospect theory. It also offers a critique of prospect theory and goes on to discuss Allais's interpretation of his paradox, paying special attention to his invariant cardinal utility function. The chapter concludes with an assessment of the utility of a risky prospect.Less
This chapter focuses on the psychological importance of downside risk by presenting Maurice Allais's paradox and by contrasting how Allais and prospect theory have interpreted this paradox. It also considers whether the HRL formulation can be used to model how financial market participants form “expectations” of the dispersion of returns under uncertainty. The chapter begins with a brief overview of expected utility theory, with particular emphasis on the Saint Petersburg paradox and how it was resolved by Daniel Bernoulli in 1738. It then considers the Allais paradox and its conflicting interpretations, including prospect theory. It also offers a critique of prospect theory and goes on to discuss Allais's interpretation of his paradox, paying special attention to his invariant cardinal utility function. The chapter concludes with an assessment of the utility of a risky prospect.
Jennifer Coopersmith
- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198716747
- eISBN:
- 9780191800955
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198716747.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics
Connections between ‘airs’ and heat emerged. Hales, in Vegetable Staticks, liberated ‘airs’ on heating various substances, and concluded that there was a repulsive force in ‘elastick air’. This was ...
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Connections between ‘airs’ and heat emerged. Hales, in Vegetable Staticks, liberated ‘airs’ on heating various substances, and concluded that there was a repulsive force in ‘elastick air’. This was consistent with a speculation of Newton’s, and with Boyle’s ‘spring of the air’. Thus, a static model of gas pressure was developed. Boerhaave had ‘fire’ as a universal causal agent and established the morphology of heat studies. He initiated the material (substance or subtle-fluid) theory of heat, but rejected the contemporaneous phlogiston theory. Daniel Bernoulli proposed a kinetic theory of gases (in Hydrodynamica) and calculated the ‘live force contained within an elastic fluid’. The iconic formula, PdV, could be glimpsed for the first time. Also, Amontons’ experimental finding—that pressure is proportional to temperature—was given a theoretical underpinning. Newcomen’s revolutionary atmospheric engine was the first true steam engine, with a piston in a cylinder and valves, and truly self-acting.Less
Connections between ‘airs’ and heat emerged. Hales, in Vegetable Staticks, liberated ‘airs’ on heating various substances, and concluded that there was a repulsive force in ‘elastick air’. This was consistent with a speculation of Newton’s, and with Boyle’s ‘spring of the air’. Thus, a static model of gas pressure was developed. Boerhaave had ‘fire’ as a universal causal agent and established the morphology of heat studies. He initiated the material (substance or subtle-fluid) theory of heat, but rejected the contemporaneous phlogiston theory. Daniel Bernoulli proposed a kinetic theory of gases (in Hydrodynamica) and calculated the ‘live force contained within an elastic fluid’. The iconic formula, PdV, could be glimpsed for the first time. Also, Amontons’ experimental finding—that pressure is proportional to temperature—was given a theoretical underpinning. Newcomen’s revolutionary atmospheric engine was the first true steam engine, with a piston in a cylinder and valves, and truly self-acting.
Paul Schmid-Hempel
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199229482
- eISBN:
- 9780191774744
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199229482.003.0011
- Subject:
- Biology, Disease Ecology / Epidemiology, Evolutionary Biology / Genetics
This chapter discusses ‘epidemiology’, which in medical literature refers to the field that seeks to identify key correlates for a particular disease. In this book, however, it is the study of ...
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This chapter discusses ‘epidemiology’, which in medical literature refers to the field that seeks to identify key correlates for a particular disease. In this book, however, it is the study of host–parasite population dynamics as a branch of population biology and population genetics. Beginning with the Swiss mathematician Daniel Bernoulli, who used a mathematical model to analyse the dynamics of a small-pox epidemic in Paris, epidemiology provides a great help to the study of evolutionary parasitology. The classical Nicholson-Bailey model is one example of an epidemiology model that analyses host–parasitoid systems. The chapter examines other models, such as SIR-models, in order to further analyse the epidemiology of hosts and their microparasites. It also talks about the epidemiology of vectored microparasites, like malaria, which can also similarly be analysed with modified SIR-models such as the classical Ross-Macdonald model.Less
This chapter discusses ‘epidemiology’, which in medical literature refers to the field that seeks to identify key correlates for a particular disease. In this book, however, it is the study of host–parasite population dynamics as a branch of population biology and population genetics. Beginning with the Swiss mathematician Daniel Bernoulli, who used a mathematical model to analyse the dynamics of a small-pox epidemic in Paris, epidemiology provides a great help to the study of evolutionary parasitology. The classical Nicholson-Bailey model is one example of an epidemiology model that analyses host–parasitoid systems. The chapter examines other models, such as SIR-models, in order to further analyse the epidemiology of hosts and their microparasites. It also talks about the epidemiology of vectored microparasites, like malaria, which can also similarly be analysed with modified SIR-models such as the classical Ross-Macdonald model.
- Published in print:
- 2008
- Published Online:
- March 2013
- ISBN:
- 9780226709321
- eISBN:
- 9780226709338
- Item type:
- chapter
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226709338.003.0007
- Subject:
- History, Environmental History
It was local tide calculators, not elite theorists, who advanced the study of the tides in the late eighteenth and early nineteenth centuries, perfecting Daniel Bernoulli's equilibrium theory through ...
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It was local tide calculators, not elite theorists, who advanced the study of the tides in the late eighteenth and early nineteenth centuries, perfecting Daniel Bernoulli's equilibrium theory through their own extended observations. In fact, the tide tables in port cities such as Liverpool and Bristol were exceedingly, even exceptionally, accurate. This chapter analyzes William Whewell's close collaboration with those practitioners he termed “subordinate laborers,” a diverse group who worked alongside the scientific servicemen and scientific elite. In particular, it focuses on the contributions of expert calculators to large-scale geophysical research. Not only were these diligent men of numbers the first to bring the data to the natural philosophers, but they first applied the results to the construction of tables, and thus to the testing of theory. Their ingenuity with difficult calculations made them indispensable for Whewell's tidology. Though they began as calculators Whewell desired “to keep at work,” they actively contributed to his tidology: they tested his theories, advanced his methods, and suggested new avenues of research.Less
It was local tide calculators, not elite theorists, who advanced the study of the tides in the late eighteenth and early nineteenth centuries, perfecting Daniel Bernoulli's equilibrium theory through their own extended observations. In fact, the tide tables in port cities such as Liverpool and Bristol were exceedingly, even exceptionally, accurate. This chapter analyzes William Whewell's close collaboration with those practitioners he termed “subordinate laborers,” a diverse group who worked alongside the scientific servicemen and scientific elite. In particular, it focuses on the contributions of expert calculators to large-scale geophysical research. Not only were these diligent men of numbers the first to bring the data to the natural philosophers, but they first applied the results to the construction of tables, and thus to the testing of theory. Their ingenuity with difficult calculations made them indispensable for Whewell's tidology. Though they began as calculators Whewell desired “to keep at work,” they actively contributed to his tidology: they tested his theories, advanced his methods, and suggested new avenues of research.
Gilles Bénéplanc and Jean-Charles Rochet
- Published in print:
- 2011
- Published Online:
- April 2015
- ISBN:
- 9780199774081
- eISBN:
- 9780190258474
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:osobl/9780199774081.003.0009
- Subject:
- Business and Management, Finance, Accounting, and Banking
This chapter talks about the expected utility criterion, which solves the St Petersburg paradox proposed in the 18th century by Nicolas Bernoulli. The criterion is useful in modeling insurance ...
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This chapter talks about the expected utility criterion, which solves the St Petersburg paradox proposed in the 18th century by Nicolas Bernoulli. The criterion is useful in modeling insurance decisions and modeling equilibrium prices in the markets where risks are exchanged. However, the equilibrium approach to the assessment of risk premiums has its limits and does not match the observed behavior of individuals who are uncertain about the probability distributions of risks.Less
This chapter talks about the expected utility criterion, which solves the St Petersburg paradox proposed in the 18th century by Nicolas Bernoulli. The criterion is useful in modeling insurance decisions and modeling equilibrium prices in the markets where risks are exchanged. However, the equilibrium approach to the assessment of risk premiums has its limits and does not match the observed behavior of individuals who are uncertain about the probability distributions of risks.
