We investigate an optimal portfolio and consumption choice problem with a defaultable security. Under the goal of maximizing the expected discounted utility of the average past consumption, a dynamic programming principle is applied to derive a pair of second-order parabolic Hamilton-Jacobi- Bellman (HJB) equations with gradient constraints. We explore these HJB equations by a viscosity solution approach and characterize the post-default and pre-default value functions as a unique pair of constrained viscosity solutions to the HJB equations.
We first propose a new class of smoothing functions for the nonlinear complementarity function which contains the well-known Chen-Harker- Kanzow-Smale smoothing function and Huang-Han-Chen smoothing function as special cases, and then present a smoothing inexact Newton algorithm for the
Weak log-Sobolev and
In this paper, using generating functions, we study two categories
This paper is a further contribution to the classification of linetransitive finite linear spaces. We prove that if
We consider the
We first prove a basic theorem with respect to the moving frame along a Lagrangian immersion into the complex projective space
This work is mainly concerned with the rotating Newtonian stars with prescribed angular velocity law. For general compressible fluids, the existence of rotating star solutions was proved by using concentrationcompactness principle. In this paper, we establish the asymptotic estimates on the diameters of the stars with small rotation. The novelty of this paper is that a direct and concise definition of
The linear third-order ordinary differential equation (ODE) can be transformed into a system of two second-order ODEs by introducing a variable replacement, which is different from the common order-reduced approach. We choose the functions
Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321: 3601-3619] constructed a new family of finite-dimensional modular Lie superalgebra
Let
In this paper, we consider the lattice Schr¨odinger equations