2,892 research outputs found
Necessary Condition for Near Optimal Control of Linear Forward-backward Stochastic Differential Equations
This paper investigates the near optimal control for a kind of linear
stochastic control systems governed by the forward backward stochastic
differential equations, where both the drift and diffusion terms are allowed to
depend on controls and the control domain is not assumed to be convex. In the
previous work (Theorem 3.1) of the second and third authors [\textit{%
Automatica} \textbf{46} (2010) 397-404], some problem of near optimal control
with the control dependent diffusion is addressed and our current paper can be
viewed as some direct response to it. The necessary condition of the
near-optimality is established within the framework of optimality variational
principle developed by Yong [\textit{SIAM J. Control Optim.} \textbf{48} (2010)
4119--4156] and obtained by the convergence technique to treat the optimal
control of FBSDEs in unbounded control domains by Wu [% \textit{Automatica}
\textbf{49} (2013) 1473--1480]. Some new estimates are given here to handle the
near optimality. In addition, an illustrating example is discussed as well.Comment: To appear in International Journal of Contro
Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model
This paper considers a portfolio optimization problem in which asset prices
are represented by SDEs driven by Brownian motion and a Poisson random measure,
with drifts that are functions of an auxiliary diffusion factor process. The
criterion, following earlier work by Bielecki, Pliska, Nagai and others, is
risk-sensitive optimization (equivalent to maximizing the expected growth rate
subject to a constraint on variance.) By using a change of measure technique
introduced by Kuroda and Nagai we show that the problem reduces to solving a
certain stochastic control problem in the factor process, which has no jumps.
The main result of the paper is to show that the risk-sensitive jump diffusion
problem can be fully characterized in terms of a parabolic
Hamilton-Jacobi-Bellman PDE rather than a PIDE, and that this PDE admits a
classical C^{1,2} solution.Comment: 33 page
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