Multiperiod competition with switching costs: solutions by Lagrange multipliers

Article Abstract:

Lagrange multipliers are applied to solve problems of dynamic games of Beggs and Klemperer on price determination of duopolists whose market incurs consumer switching costs. The study suggests that this method is more convenient than dynamic programming. It is assumed first that consumers are myopic and choose products based on current prices. Then, they are allowed to consider future prices. Solutions prove that the method is simpler than dynamic programming due to lesser parameters to solve.

Duopolies

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Chow's method of optimal control: a numerical solution

Article Abstract:

The numerical solution suggested by Chow (1993) in solving dynamic optimization problems can be approached through the Lagrange multiplier. The approach approximates the optimal control and the related Lagrange functions by multi-variate linearization in a steady state to obtain the optimal control function. The result is a linear optimal control function that can be used globally to approximate the optimal control functions of other state variables.

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

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The Lagrange method of optimization with applications to portfolio and investment decisions

Article Abstract:

An alternative to dynamic programming is developed for solving dynamic optimization problems that involve stochastic differential equations. The new approach, a method of Lagrange multipliers, generalizes Pontryagin's maximum principle to stochastic models. When applied in stochastic cases, it is analytically simpler and computationally more accurate than dynamic programming.

Methods, Portfolio management, Stochastic processes

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