Dynamic programming for non-additive stochastic objectives

Article Abstract:

The existence of an optimum and dynamic programming techniques was derived from abstract assumptions based on primitive utility function U and its W and M primitive aggregators. A non-positive-valued utility function U that is derived from a W dynamic aggregator and an M stochastic aggregator was constructed. The resulting examples exhibit mean growth without the distribution of unbounded support due to the few growth restrictions of non-positive objectives.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Methods, Stochastic analysis

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A strategic market game with secured lending

Article Abstract:

Using one durable commodity, borrowing/lending through a money market or central bank, and a continuum of agents, stationary mark or equilibria for strategic, competitive games in the context of a market economy are studied to establish general theorems while opening up other areas for further inquiry. The Markov chains' invariant measures are studied in detail together with each agents' dynamic optimization problems.

Banking Institutions, Depository Credit Intermediation, DEPOSITORY INSTITUTIONS, Banks (Finance), Capitalism, Loans, Markov processes

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An abstract topological approach to dynamic programming

Article Abstract:

The traditional approach to the mathematical theory of dynamic programming incorporates an abstract contraction property known as Lipschitz condition. Biconvergence is a suggested alternative approach that embodies an abstract topological condition on both the utility function and the intertemporal production correspondence. Biconvergence is easier to test, and results are less difficult to interpret.

Usage, Topology, Convergence (Mathematics), Utility theory, Utility functions

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