In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime s...

An easy-to-use variant of the finite difference method (FDM), the polynomial finite difference method (PFDM), for the numerical solution of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs), is presented. Compared to the traditional implementation of the FDM, the PFDM approach has two major advantages: straightforward implementation, and easily adjustable accura...

In this paper, some properties of all positive solutions are considered for a higher order rational difference equation, mainly for the existence of eventual prime period two solutions, the existence and asymptotic behavior of nonoscillatory solutions and the global asymptotic stability of its equilibria. Our results show that a positive equilibrium point of this equation is a global attractor ...

For any integer m let P (m) denote the greatest prime factor of m and let Q(m) denote the greatest square free factor of m with the convention that P (0) = P (±1) = 1 = Q(±1) = Q(0). Thus, if m = p1 1 · · · p hr r with p1, . . . , pr distinct primes and h1, . . . , hr positive integers, then Q(m) = p1 · · · pr. van der Poorten and Schlickewei [6] and Evertse [1] proved, by means of a p-adic ver...

Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G. AMS Subject Classifications: 15A15, 39A06, 92D25,39A06.