43,377 research outputs found
Optimal probabilities and controls for reflecting diffusion processes
A solution to the optimal problem for determining vector fields which
maximize (resp. minimize) the transition probabilities from one location to
another for a class of reflecting diffusion processes is obtained in the
present paper. The approach is based on a representation for the transition
probability density functions. The optimal transition probabilities under the
constraint that the drift vector field is bounded by a constant are studied in
terms of the HJB equation. In dimension one, the optimal reflecting diffusion
processes and the bang-bang diffusion processes are considered. We demonstrate
by simulations that, even in this special case, the optimal diffusion processes
exhibit an interesting feature of phase transitions. We also solve an optimal
stochastic control problem for a class of stochastic control problems involving
diffusion processes with reflection.Comment: 20 Pages, 2 figure
Why Chinas Economic Reforms Differ: The M-Form Hierarchy and Entry/Expansion of the Non-State Sector
China's thirteen years of reforms (1979-1991) have achieved an average GNP annual growth rate of 8.6%. What makes China's reforms from those of Eastern Europe and the Soviet Union is the sustained entry and expansion of the non-state sector. We argue that the organization structure of the economy matters. Unlike their unitary hierarchical structure based on the functional or specialization principles (the U-form), China's hierarchical economy has been the multi-layer-multi-regional one mainly based on territorial principle (the deep M-form, or briefly, the M-form). Reforms have further decentralized the M-form economy along regional lines, which provided flexibility and opportunities for carrying out regional experiments, for the rise of non-state enterprises, and for the emergence of markets. This is why China's non-state sector share of industrial output increased from 22% in 1978 to 47% in 1991 and its private sector's share from zero to about 10%, both being achieved without mass privatization and changes in the political system.
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