scholarly journals A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization

2010 ◽  
Vol 72 (2) ◽  
pp. 273-310 ◽  
Author(s):  
Daniel Andersson ◽  
Boualem Djehiche
Keyword(s):  
Maximum Principle ◽  
Portfolio Optimization ◽  
Stochastic Control ◽  
Bond Portfolio

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.

Anticipative portfolio optimization

1996 ◽  
Vol 28 (04) ◽  
pp. 1095-1122 ◽  
Author(s):  
Igor Pikovsky ◽  
Ioannis Karatzas
Keyword(s):  
Brownian Motion ◽  
Control Problem ◽  
Closed Form ◽  
Portfolio Optimization ◽  
Stochastic Control ◽  
Financial Economics ◽  
Optimal Portfolio ◽  
The Novel ◽  
Terminal Wealth ◽  
Terminal Values

We study a classical stochastic control problem arising in financial economics: to maximize expected logarithmic utility from terminal wealth and/or consumption. The novel feature of our work is that the portfolio is allowed to anticipate the future, i.e. the terminal values of the prices, or of the driving Brownian motion, are known to the investor, either exactly or with some uncertainty. Results on the finiteness of the value of the control problem are obtained in various setups, using techniques from the so-called enlargement of filtrations. When the value of the problem is finite, we compute it explicitly and exhibit an optimal portfolio in closed form.

scholarly journals A Maximum Principle for Stochastic Control with Partial Information

2007 ◽  
Vol 25 (3) ◽  
pp. 705-717 ◽  
Author(s):  
Fouzia Baghery ◽  
Bernt Øksendal
Keyword(s):  
Maximum Principle ◽  
Stochastic Control ◽  
Partial Information
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