Verification Theorem Of Stochastic Optimal Control With Mixed Delay And Applications To Finance

2014 ◽  
Vol 17 (4) ◽  
pp. 1285-1295 ◽  
Author(s):  
Wenli Zhu ◽  
Zisha Zhang
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Verification Theorem ◽  
Mixed Delay

Stochastic Optimal Control

2019 ◽  
pp. 333-350
Author(s):  
Tomas Björk
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Verification Theorem ◽  
Stochastic Optimal Control Problem ◽  
Hamilton Jacobi Bellman

We study a general stochastic optimal control problem within the framework of a controlled SDE. This problem is studied using dynamic programming and we derive the Hamilton–Jacobi–Bellman PDE. By stating and proving a verification theorem we show that solving this PDE is equivalent to solving the control problem. As an example the theory is then applied to the linear quadratic regulator.

scholarly journals BSDEs with Logarithmic Growth Driven by Brownian Motion and Poisson Random Measure and Connection to Stochastic Control Problem

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Khalid Oufdil
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Random Measure ◽  
Poisson Random Measure ◽  
One Dimensional ◽  
Stochastic Optimal Control Problem ◽  
Uniqueness Of The Solution ◽  
Logarithmic Growth

Abstract In this paper, we study one-dimensional backward stochastic differential equations under logarithmic growth in the 𝑧-variable ( | z | ⁢ | ln ⁡ | z | | ) (\lvert z\rvert\sqrt{\lvert\ln\lvert z\rvert\rvert}) . We show the existence and the uniqueness of the solution when the noise is driven by a Brownian motion and an independent Poisson random measure. In addition, we highlight the connection of such BSDEs with stochastic optimal control problem, where we show the existence of an optimal strategy for the control problem.

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