Leontief systems, RBV’s and RBM’s. (English) Zbl 0729.90021
Applied stochastic analysis, Pap. Workshop, London/UK 1989, Stochastic Monogr. 5, 1-43 (1990).
Summary: [For the entire collection see Zbl 0728.00017.]
A stochastic continuous-time input-output model is proposed, which is an analog of the classical Leontief system in economics. Feasibility and efficiency results are established in terms of a dynamic version of the linear complementarity problem from mathematical programming. Solving this dynamic version amounts to subjecting a given process to oblique reflection on an orthant or a simplex. Explicitly considered are reflected processes of bounded variation (RBV’s), and reflected Brownian motions (RBM’s). It is explained how RBM’s arise as diffusion approximations to Leontief systems, when the latter are heavily-loaded and driven by RBV’s.
A stochastic continuous-time input-output model is proposed, which is an analog of the classical Leontief system in economics. Feasibility and efficiency results are established in terms of a dynamic version of the linear complementarity problem from mathematical programming. Solving this dynamic version amounts to subjecting a given process to oblique reflection on an orthant or a simplex. Explicitly considered are reflected processes of bounded variation (RBV’s), and reflected Brownian motions (RBM’s). It is explained how RBM’s arise as diffusion approximations to Leontief systems, when the latter are heavily-loaded and driven by RBV’s.
MSC:
| 91B62 | Economic growth models |
| 93E03 | Stochastic systems in control theory (general) |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 91B66 | Multisectoral models in economics |
| 90C90 | Applications of mathematical programming |
