Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation†

Maximin setting for investment problems and fixed income management with observable but non-predictable parameters

We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is described by Itô’s equation, and the number of risky assets can be larger than the number of driving Brownian motions. We assume that the risk-free rate, the appreciation rates and the volatility of the stocks are all random...

Topological Pressure via Saddle Points

Let Λ be a compact locally maximal invariant set of a C2diffeomorphism f : M → M on a smooth Riemannian manifold M . In this paper we study the topological pressure Ptop(φ) (with respect to the dynamical system f |Λ) for a wide class of Hölder continuous potentials and analyze its relation to dynamical, as well as geometrical, properties of the system. We show that under a mild non-uniform hype...

Solution for the Heat Equation

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

Numerical solution of saddle point problems

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been prop...