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where r is the risk-free rate, (μ, σ) are the expected return and volatility of the stock market and dB t is the increment of the Wiener process, i.e. the stochastic term of the SDE. The utility function is of the constant relative risk aversion (CRRA) form: =.
The classic counter example to the expected value theory (where everyone makes the same "correct" choice) is the St. Petersburg Paradox. [3] In empirical applications, several violations of expected utility theory are systematic, and these falsifications have deepened our understanding of how people decide.
An example of how indifference curves are obtained as the level curves of a utility function. A graph of indifference curves for several utility levels of an individual consumer is called an indifference map. Points yielding different utility levels are each associated with distinct indifference curves and these indifference curves on the ...
Right graph: With fixed probabilities of two alternative states 1 and 2, risk averse indifference curves over pairs of state-contingent outcomes are convex. In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter ...
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Supporters of cardinal utility theory in the 19th century suggested that market prices reflect utility, although they did not say much about their compatibility (i.e., prices being objective while utility is subjective). Accurately measuring subjective pleasure (or pain) seemed awkward, as the thinkers of the time were surely aware.
An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data.. In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
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