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In this paper, the mean square exponential stability of a class of stochastic Hopfield neural networks with mixed delays is investigated. Employing Itô’s formula and applying the inequality techniques, a sufficient condition ensuring mean square exponential stability is proved. The main result derived in this paper generalizes the results in Wan and Sun (2005), Sun and Cao (2007) and Zhu and Cao (2014) etc. An example is also given to illustrate the main result. [ABSTRACT FROM AUTHOR]

This paper considers a variant of Itô's formula for discontinuous semimartingales and non- C 2 functions. This result is particularly helpful for insurance control problems with Markov-modulated components. An example of a dividend barrier strategy for a Brownian risk model with Markov-switching illustrates the result. [ABSTRACT FROM AUTHOR]