Relative optimization of continuous-time and continuous-state stochastic systems (Q2173468)

For discrete settings theory and application of relative optimization has already been fairly well developed. The purpose of the present volume is the extension to continuous-state and continuous-time stochastic systems, taking an engineering point of view, avoiding heavy mathematical technicalities such as the existence and uniqueness of solutions of partial differential equations or the theory of viscosity solutions, as they occur in the context of dynamic programming. The author begins by explaining and exemplifying the difference between the latter and relative optimization: While dynamic programming provides the ``local'' information about the value function at a particular state and time, relative optimization leads to the ``global'' information about the performance comparison in the entire time horizon. The introduction is followed by chapters on optimal control of Markov processes with infinite horizon, on optimal control of diffusion processes, degenerate diffusions, and multi-dimensional diffusions, and on performance-derivative based optimization. Most of the new results in the book concern cases in which the value function or potential function is semi-smooth, i.e., at some point their two one-sided first-order derivatives exist but are not equal. Also, the under-selectivity issue for long-run average optimization is solved. Mathematical tools needed, mostly from stochastic analysis, are provided, and each chapter contains examples and exercises, with solutions given at the end of the book.