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Finding (,) is the utility maximization problem. If u is continuous and no commodities are free of charge, then x ( p , I ) {\displaystyle x(p,I)} exists, [ 4 ] but it is not necessarily unique. If the preferences of the consumer are complete, transitive and strictly convex then the demand of the consumer contains a unique maximiser for all ...
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social ...
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice.An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility.
In order to compare the different decision outcomes, one commonly assigns a utility value to each of them. If there is uncertainty as to what the outcome will be but one has knowledge about the distribution of the uncertainty, then under the von Neumann–Morgenstern axioms the optimal decision maximizes the expected utility (a probability ...
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility function.
Consider the portfolio allocation problem of maximizing expected exponential utility [] of final wealth W subject to = ′ + (′) where the prime sign indicates a vector transpose and where is initial wealth, x is a column vector of quantities placed in the n risky assets, r is a random vector of stochastic returns on the n assets, k is a vector of ones (so ′ is the quantity placed in the ...
For example, if someone chooses consumption, given wealth, in order to maximize happiness (assuming happiness H can be represented by a mathematical function, such as a utility function and is something defined by wealth), then each level of wealth will be associated with some highest possible level of happiness, ().
The utility functions may represent their chance of recovery – () is the probability of agent to recover by getting doses of the medication. The utilitarian rule then allocates the medication in a way that maximizes the expected number of survivors.