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In economics, a random utility model (RUM), [1] [2] also called stochastic utility model, [3] is a mathematical description of the preferences of a person, whose choices are not deterministic, but depend on a random state variable.
The term stochastic process first appeared in English in a 1934 paper by Joseph L. Doob. [1] For the term and a specific mathematical definition, Doob cited another 1934 paper, where the term stochastischer Prozeß was used in German by Aleksandr Khinchin, [22] [23] though the German term had been used earlier in 1931 by Andrey Kolmogorov. [24]
Stochastic dominance is a partial order between random variables. [1] [2] It is a form of stochastic ordering.The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers.
In the case where the maximization is an integral of a concave function of utility over an horizon (0,T), dynamic programming is used. There is no certainty equivalence as in the older literature, because the coefficients of the control variables—that is, the returns received by the chosen shares of assets—are stochastic.
The definition of a stochastic process varies, [67] but a stochastic process is traditionally defined as a collection of random variables indexed by some set. [68] [69] The terms random process and stochastic process are considered synonyms and are used interchangeably, without the index set being precisely specified.
Here, the intuition is the same as in the construction of the traditional maximum score estimator: the agent is more likely to choose the choice that has the higher observed part of latent utility. Under certain conditions, the smoothed maximum score estimator is consistent, and more importantly, it has an asymptotic normal distribution.
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Markov decision process (MDP), also called a stochastic dynamic program or stochastic control problem, is a model for sequential decision making when outcomes are uncertain. [ 1 ] Originating from operations research in the 1950s, [ 2 ] [ 3 ] MDPs have since gained recognition in a variety of fields, including ecology , economics , healthcare ...