11 research outputs found
On Necessary and Sufficient Conditions for Near-Optimal Singular Stochastic Controls
This paper is concerned with necessary and sufficient conditions for
near-optimal singular stochastic controls for systems driven by a nonlinear
stochastic differential equations (SDEs in short). The proof of our result is
based on Ekeland's variational principle and some delicate estimates of the
state and adjoint processes. This result is a generalization of Zhou's
stochastic maximum principle for near-optimality to singular control problem.Comment: 19 pages, submitted to journa
On Peng's type maximum principle for optimal control of mean-field stochastic differential equations with jump processes
On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance
summary:We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum condition on the Hamiltonian function is a sufficient condition for near-optimality. At the end, as an application to finance, mean-variance portfolio selection mixed with a recursive utility optimization problem is given
Dynamical Study of Fractional Model of Allelopathic Stimulatory Phytoplankton Species
In this paper, we present a fractional model of interacting phytoplankton species in which one species produces chemical which is stimulatory in nature to the other species. We study existence, uniqueness, permanence, persistence and stability of the solution. We introduce a new method to prove permanence and persistence, which may be applicable to several ecological models of fractional order. At the end we propose a discritization method and perform some numerical simulations to validate our analytical findings
Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order α ∈ ( 0 , 1 ) . Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover, we establish the approximate controllability of the problem by applying a unique continuation property via internal control which acts on a sub-domain