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Portfolio optimization is the process of selecting an optimal portfolio (asset distribution), out of a set of considered portfolios, according to some objective.The objective typically maximizes factors such as expected return, and minimizes costs like financial risk, resulting in a multi-objective optimization problem.
Somewhat surprisingly for an optimal control problem, a closed-form solution exists. The optimal consumption and stock allocation depend on wealth and time as follows: [4]: 401 (,) =. This expression is commonly referred to as Merton's fraction.
In a general context the optimal portfolio allocation in any time period after the first will depend on the amount of wealth that results from the previous period's portfolio, which depends on the asset returns that occurred in the previous period as well as that period's portfolio size and allocation, the latter having depended in turn on the amount of wealth resulting from the portfolio of ...
The amount of information (the covariance matrix, specifically, or a complete joint probability distribution among assets in the market portfolio) needed to compute a mean-variance optimal portfolio is often intractable and certainly has no room for subjective measurements ('views' about the returns of portfolios of subsets of investable assets ...
The Partial Allocation Mechanism (PAM) is a mechanism for truthful resource allocation.It is based on the max-product allocation - the allocation maximizing the product of agents' utilities (also known as the Nash-optimal allocation or the Proportionally-Fair solution; in many cases it is equivalent to the competitive equilibrium from equal incomes).
The ratio for two agents and two resources improved from 0.828 to 5/6 ≈ 0.833 with a complete-allocation mechanism, and strictly more than 5/6 with a partial-allocation mechanism. The upper bound improved from 0.841 to 5/6+ε for a complete-allocation mechanism, and to 0.8644 for a partial mechanism.
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Linear programming (LP), originally developed and commonly used for optimal allocation of scarce resources, is the primary mathematical tool of Enterprise Optimization. Concepts [ edit ]