BSDEs with logarithmic growth driven by a Brownian motion and a Poisson\n random measure and connection to stochastic control problem

In this paper, we study one-dimensional backward stochastic differential\nequation with jump under logarithmic growth assumption in the z-variable\n(|z|\\sqrt{|\\ln|z|}|) and an L^p terminal value (for a suitable p>2). We show\nthe existence and the uniqueness of the solution when the noise is driven by a\nBrownian motion and an independent Poisson random measure. In addition, we\nhighlight the connection of such BSDEs with stochastic optimal control problem,\nwhere we show the existence of an optimal strategy for the stochastic control\nproblem.\n