On a conditioned Brownian motion and a maximum principle on the disk

2004 ◽  
Vol 93 (1) ◽  
pp. 309-329 ◽  
Author(s):  
A. Dall'Acqua ◽  
H. -C. Grunau ◽  
G. H. Sweers
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Conditioned Brownian Motion

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

2020 ◽  
Vol 28 (4) ◽  
pp. 291-306
Author(s):  
Tayeb Bouaziz ◽  
Adel Chala
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Control Problem ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Malliavin Calculus ◽  
Stochastic Maximum Principle ◽  
Hurst Parameter ◽  
Principle Of Optimality ◽  
Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

scholarly journals A stochastic maximum principle for processes driven by fractional Brownian motion

2002 ◽  
Vol 100 (1-2) ◽  
pp. 233-253 ◽  
Author(s):  
Francesca Biagini ◽  
Yaozhong Hu ◽  
Bernt Øksendal ◽  
Agnès Sulem
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Fractional Brownian Motion ◽  
Stochastic Maximum Principle
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