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.