An introduction to stochastic processes by D. Kannan

By D. Kannan

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Savage (1954) comments on an exchange between Gabriel Cramer and Daniel Bernoulli’s uncle Nicholas Bernoulli on this issue: Daniel Bernoulli’s paper reproduces portions of a letter from Gabriel Cramer to Nicholas Bernoulli, which establishes Cramer’s chronological priority to the idea of utility and most of the other main ideas of Bernoulli’s paper. . Cramer pointed out in his aforementioned letter, the logarithm has a serious disadvantage; for, if the logarithm were the utility of wealth, the St.

Several statistics books have good chapters on decision-theoretic topics. Excellent examples are Schervish (1995) and Robert (1994), both very rigorous and rich in insightful examples. Bernardo and Smith (1994) is also rich in foundational discussions presented in the context of both statistical inference and decision theory. French (1988), Smith (1987), and Bather (2000) cover decision-analytic topics very well. Kreps (1988) is an accessible and very insightful discussion of foundations, covered in good technical detail.

The birthplace of utility theory is usually considered to be St. Petersburg. In 1738, Daniel Bernoulli, a Swiss mathematician who held a chair at the local Academy of Science, published a very influential paper on decision making (Bernoulli 1738). Bernoulli analyzed the behavior of rational individuals in the face of uncertainty from a Newtonian perspective, viewing science as an operational model of the human mind. His empirical observation, that thoughtful individuals do not necessarily take the financial actions that maximize their expected monetary return, led him to investigate a formal model of individual choices based on the direct quantification of value, and to develop a prototypical utility function for wealth.

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