Relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problems of jump diffusions and applications to finance

2010 ◽  
Author(s):  
Jingtao Shi
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Dynamic Programming Principle ◽  
Control Problems ◽  
Jump Diffusions

scholarly journals Relationship between Maximum Principle and Dynamic Programming for Stochastic Recursive Optimal Control Problems and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jingtao Shi ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Hamiltonian Function ◽  
Control Problems ◽  
Linear Quadratic ◽  
Portfolio Optimization Problem ◽  
The Relationship ◽  
The Value Function

This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.

scholarly journals On the time discretization of stochastic optimal control problems: The dynamic programming approach

2019 ◽  
Vol 25 ◽  
pp. 63 ◽  
Author(s):  
Joseph Frédéric Bonnans ◽  
Justina Gianatti ◽  
Francisco J. Silva
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Discrete Time ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Time Discretization ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Control Problems ◽  
Discrete Problems

In this work, we consider the time discretization of stochastic optimal control problems. Under general assumptions on the data, we prove the convergence of the value functions associated with the discrete time problems to the value function of the original problem. Moreover, we prove that any sequence of optimal solutions of discrete problems is minimizing for the continuous one. As a consequence of the Dynamic Programming Principle for the discrete problems, the minimizing sequence can be taken in discrete time feedback form.

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