The following chapter can be understood as one sort of brief introduction to the history and basics of the Hidden Markov Models. Hidden Markov Models (HMMs) are learnable finite stochastic automates. Nowadays, they are considered as a specific form of dynamic Bayesian networks. Dynamic Bayesian networks are based on the theory of Bayes (Bayes & Price, 1763). A Hidden Markov Model consists of tw...

We study dynamic signaling in a game of stochastic stakes. Each period, privately informed agent binary type chooses whether to continue receiving return that is an increasing function both her reputation and exogenous public stakes variable or irreversibly exit the game. A strong has dominant strategy continue. In unique perfect Bayesian equilibrium, weak plays mixed depends only on current hi...

We introduce Stochastic Dynamic Cutting Plane (StoDCuP), an extension of the Dual Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, builds lower bounding affine functions not only for cost-to-go functions, as SDDP does, but also some or all nonlinear cost and constraint functions. show almost sure convergence StoDCuP. inexact variant St...