John van der Hoek

A GENERAL FRACTIONAL WHITE NOISE THEORY AND APPLICATIONS TO FINANCE

We present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure. Our results extend recent contributions by Hu, Oksendal, Duncan, Pasik-Duncan, and others. As an application we develop option pricing in a fractional Black-Scholesmarket with a noise process driven by a sum of fractional Brownian motions with various Hurst indices.

A Galerkin procedure for the diffusion equation subject to the specification of mass

Continuous and discrete Galerkin procedures are derived and analyzed for the numerical solution of the diffusion equation

Diffusion subject to the specification of mass

U_1 = U_{xx} ,0 < x < 1,0 < t \leqq T,U(x,0) = f(x),U_x (1,t) = g(t)

An application of hidden Markov models to asset allocation problems

and the specification of the mass

Stochastic flows and the forward measure

\int _0^b U(x,t)dx = M(t),0 < b < 1

The classical solution of the one-dimensional two-phase stefan problem with energy specification

. Some numerical experiments are also presented.

A class of non-expected utility risk measures and implications for asset allocations

Abstract Existence, uniqueness, and continuous dependence upon the data are demonstrated for the solution u = u(x, t) of the diffusion equation ut = uxx + s(x, t), 0 u(x, 0) = ƒ(x), 0 , ux(1, t) = g(t), 0 ∫ 0 b(0) ƒ(x) dx = m(0) . A numerical procedure is discussed and results of numerical experiments are presented.

Existence and uniqueness of generalized vortices

Abstract. Filtering and parameter estimation techniques from hidden Markov Models are applied to a discrete time asset allocation problem. For the commonly used mean-variance utility explicit optimal strategies are obtained.

Space matters: the importance of amenity in planning metropolitan growth

Abstract. Stochastic flows and their Jacobians are used to show why, when the short rate process is described by Gaussian dynamics, (as in the Vasicek or Hull-White models), or square root, affine (Bessel) processes, (as in the Cox-Ingersoll-Ross, or Duffie-Kan models), the bond price is an exponential affine function. Using the forward measure the bond price is obtained by solving a linear ordinary differential equation; Ricatti equations are not required.

Asset Pricing Using Finite State Markov Chain Stochastic Discount Functions

SummaryExistence and unicity for the solution of the one-dimensional two-phase Stefan problem with energy specification