In this paper we study utility maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding utility maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies....

We give a new proof of the fact that the value function of the finite time horizon American put option for a jump diffusion, when the jumps are from a compound Poisson process, is the classical solution of a quasi-variational inequality and it is C1 across the optimal stopping boundary. Our...

We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to a finite sequence of state-constrained optimal control...