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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]

Abstract: We prove an Itô’s formula for Walsh’s Brownian motion in the plane with angles according to a probability measure on . This extends Freidlin–Sheu formula which corresponds to the case where has finite support. We also give some applications. [Copyright &y& Elsevier]

Abstract: We present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The method of proof is based on reducing the initial problem to a free-boundary problem and solving the latter by means of the smooth-fit condition. The problem can be interpreted as pricing special perpetual average American put options in a diffusion-type model with delay. [Copyright &y& Elsevier]

Abstract: Let be the square of a ()-dimensional Bessel process starting at zero. Define iterated stochastic integrals , inductively bywith and . Then the inequalitiesandare proved to hold for all and all stopping times , where are some positive constants depending only on the subscripts, and . [Copyright &y& Elsevier]