OPTIMAL STOCHASTIC CONTROL PROBLEM UNDER MODEL UNCERTAINTY WITH NONENTROPY PENALTY

2017 ◽  
Vol 20 (03) ◽  
pp. 1750015
Author(s):  
WAHID FAIDI ◽  
ANIS MATOUSSI ◽  
MOHAMED MNIF
Keyword(s):  
Differential Equation ◽  
Control Problem ◽  
Stochastic Control ◽  
Model Uncertainty ◽  
General Framework ◽  
Backward Stochastic Differential Equation ◽  
Terminal Condition ◽  
Penalty Term ◽  
Stochastic Control Problem ◽  
Continuous Filtration

In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type [Formula: see text]-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty is studied in the context of a Brownian filtration. In the case of consistent time penalty, we characterize the value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounded terminal condition.

A Lower Bounding Linear Programming approach to the Perimeter Patrol Stochastic Control Problem

2012 ◽  
Author(s):  
Krishnamoorthy Kalyanam ◽  
Swaroop Darbha ◽  
Myoungkuk Park ◽  
Meir Pachter ◽  
Phil Chandler ◽  
...  
Keyword(s):  
Linear Programming ◽  
Control Problem ◽  
Stochastic Control ◽  
Programming Approach ◽  
Linear Programming Approach ◽  
Lower Bounding ◽  
Stochastic Control Problem

scholarly journals Mean square rate of convergence for random walk approximation of forward-backward SDEs

2020 ◽  
Vol 52 (3) ◽  
pp. 735-771
Author(s):  
Christel Geiss ◽  
Céline Labart ◽  
Antti Luoto
Keyword(s):  
Differential Equation ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Backward Stochastic Differential Equation ◽  
Stochastic Equations ◽  
Terminal Condition ◽  
Probabilistic Methods ◽  
Mean Square ◽  
Finite Difference Equations ◽  
Backward Sdes

AbstractLet (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$-convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in $C^{2,\alpha}$. The proof relies on an approximative representation of $Z^n$ and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods.

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