## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

JIMO

In this paper, the existence and stability of solutions of nonlinear optimal control problems with $1$-mean equicontinuous controls are discussed. In particular, a new existence theorem is obtained without convexity assumption. We investigate the stability of the optimal control problem with respect to the right-hand side functions, which is important in computational methods for optimal control problems when the function is approximated by a new function. Due to lack of uniqueness of solutions for an optimal control problem, the stability results for a class of optimal control problems with the measurable admissible control set is given based on the theory of set-valued mappings and the definition of essential solutions for optimal control problems. We show that the optimal control problems, whose solutions are all essential, form a dense residual set, and so every optimal control problem can be closely approximated arbitrarily by an essential optimal control problem.

DCDS-B

In this study, we establish a financial credit derivative pricing
model for a contract which is subject to counterparty risks. The
model leads to a fully nonlinear partial differential equation
problem. We study this PDE problem and obtained a solution as the
limit of a sequence of semi-linear PDE problems which also arise
from financial models. Moreover, the problems and methods build a
bridge between two main risk frameworks: structure and intensity
models. We obtain the uniqueness, regularities and some properties
of the solution of this problem.

MCRF

Traditionally, the time domains that are widely used in mathematical
descriptions are limited to real numbers for the case of
continuous-time optimal control problems or to integers for the case
of discrete-time optimal control problems. In this paper, based on a
family of "needle variations", we derive maximum principle for
optimal control problem on time scales. The results not only unify
the theory of continuous and discrete optimal control problems but
also conclude problems involving time domains in partly continuous
and partly discrete ingredients. A simple optimal control problem on
time scales is discussed in detail. Meanwhile, the results also
unify the theory of some hybrid systems, for example, impulsive
systems.

DCDS-B

This special issue of Discrete and Continuous Dynamical Systems Series B is dedicated to Professor Kok Lay Teo and Professor Jie Sun for their fundamental contributions to optimization and optimal control and their computational methods and applications. The 2010 International Conference on Optimization and Control (ICOCO2010) was held at Guizhou Park Hotel in Guiyang, China on July 18-23, 2010, in honour of Professors Teo and Sun on their 65th birthdays.

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DCDS-B

This paper introduces a new class of optimal switching problems,
where the player is allowed to switch at a sequence of exogenous
Poisson arrival times, and the underlying switching system is
governed by an infinite horizon backward stochastic differential
equation system. The value function and the optimal switching
strategy are characterized by the solution of the underlying
switching system. In a Markovian setting, the paper gives a complete
description of the structure of switching regions by means of the
comparison principle.

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