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This paper concerns continuous-time optimal investment and consumption decision of a CRRA investor who faces proportional transaction costs and finite time horizon. In the no consumption case, it has been studied by Liu and Loewenstein (2002) and Dai and Yi (2006). Mathematically, it is a singular stochastic control problem whose value function satisfies a(More)
In this paper, we discuss the evolution of the optical beam in nonlocal cubic nonlinear media, modeled by the nonlocal nonlinear Schrödinger equation (NNLSE). A different approximate model to the NNLSE is presented for the strongly nonlocal media with arbitrary response functions. An exact analytical solution of the model is obtained, and a spatial soliton(More)
This work develops a new framework for a class of stochastic control problems with optimal stopping. One of our main motivations stems from dealing with the option pricing of American type. The value function is characterized as the unique solution of a partial differential equation in a Sobolev space. Together with certain regularities and estimates of the(More)