The general approach will be described and several subclasses of problems will also be discussed including: ... H.M. Soner, N. Touzi, Stochastic Target Problems and Dynamic Programming, SIAM Journal on Control and Optimization, 41, 404–424, (2002).pdf; The auxiliary value function wis in general not smooth. 1. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Of course there is a multitude of other applications, such as optimal dividend setting, optimal entry and exit problems, utility indi erence valuation and so on. Stochastic control problems arise in many facets of nancial modelling. by Nizar Touzi. Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. time-inconsistent optimal stochastic control and optimal stopping problems. A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options A Galichon, P Henry-Labordere, N Touzi The Annals of Applied Probability 24 (1), 312-336 , 2014 Fields Institute Monographs (Book 29) Thanks for Sharing! This is a continuation of our accompanying paper [SIAM J. We study the stochastic control problem of maximizing expected utility from terminal wealth, when the wealth process is subject to shocks produced by a general marked point process; the problem of the agent is to derive the optimal allocation of his wealth between investments in a nonrisky asset and in a (costly) insurance strategy which allows “lowering” the level of the shocks. This is done by appealing to the geometric dynamic principle of Soner and Touzi [21]. The stochastic control problem (1.1) being non-standard, we rst need to establish a dynamic programming principle for optimal control under stochastic constraints. Control Optim., 54 (2016), pp. We'll publish them on our site once we've reviewed them. We develop the dynamic programming approach for the stochastic optimal control problems. 2. The second part is devoted to the class of stochastic target problems, which extends in a nontrivial way the standard stochastic control problems. The classical example is the optimal investment problem introduced and solved in continuous-time by Merton (1971). Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE. optimal stochastic control schemes within a structural reliability framework springerbriefs in statistics Oct 11, 2020 Posted By Ry?tar? We demonstrate how a time-inconsistent problem can often be re-written in terms of a sequential optimization problem involving the value function of a time-consistent optimal control problem in a higher-dimensional state-space. To give a sense to (1.6), we therefore You submitted the following rating and review. Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in Soner and Touzi (2002) , whenever the underlying filtered probability space admits a suitable martingale representation property.This provides a unified way of treating these two classes of stochastic control problems. 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