Stochastic maximum principle in the problem of optimal absolutely continuous change of measure

2006 ◽  
pp. 111-120
Author(s):  
R. J. Chitashvili
Keyword(s):  
Maximum Principle ◽  
Stochastic Maximum Principle ◽  
Continuous Change ◽  
Change Of Measure ◽  
Absolutely Continuous

scholarly journals On absolutely continuous change of measure and Markov property of stochastic processes

1969 ◽  
Vol 9 (1) ◽  
pp. 57-71
Author(s):  
B. Grigelionis
Keyword(s):  
Stochastic Processes ◽  
Markov Property ◽  
Continuous Change ◽  
Change Of Measure ◽  
Absolutely Continuous

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Григелионис. Об абсолютно непрерывной замене меры и марковском свойстве случайных процессов B. Grigelionis. Apie absoliučiai tolydinį mato pakeitimą ir atsitiktinių procesų Markovo savybę

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.

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