Piecewise Constant Policy Approximations to Hamilton-Jacobi-Bellman Equations

An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for different control parameters. Standard convergence analysis suggests that monotone (i.e., linear) interpolation must be used to transfer data between meshes. Using the equivalence to a switching system and an adaptation of the usual arguments based on consistency, stability and monotonicity, we show that if limited, potentially higher order interpolation is used for the mesh transfer, convergence is guaranteed. We provide numerical tests for the mean-variance optimal investment problem and the uncertain volatility option pricing model, and compare the results to published test cases

An Investigation of the Factor Structure of the HARVARD GROUP SCALE OF HYPNOTIC SUSCEPTIBILITY, Form A (HGSHS:A)

In order to investigate the effects of the hypnotic state a standardized hypnosis session was conducted with 144 subjects in a controlled laboratory study. The induction of a hypnotic trance in the German version of the Harvard Group Scale of Hypnotic Susceptibility (HGSHS:A by Shor and Orne, 1962) was tape-recorded and used as the treatment. The HGSHS:A seems to be a reliable measure of suggestibility and hypnotizability. This is underlined by the consistent results of a factor analysis on the depths of hypnosis that is in agreement with former studies. Descriptive data analyses with a sufficient number of subjects of high and low suggestibility suggest that our hypnosis induction by tape is an effective method of producing a hypnotic trance. Analyses of within-subjects variables did not reveal any valid predictors of hypnotizability, thereby confirming the need of screening instruments such as the HGSHS

Artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane

We discuss artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane, for a range of low Reynolds numbers. When truncating the half-plane to a finite domain for numerical purposes, artificial boundaries appear. We present an explicit Dirichlet condition for the velocity at these boundaries in terms of an asymptotic expansion for the solution to the problem. We show a substantial increase in accuracy of the computed values for drag and lift when compared with results for traditional boundary conditions. We also analyze the qualitative behavior of the solutions in terms of the streamlines of the flow. The new boundary conditions are universal in the sense that they depend on a given body only through one constant, which can be determined in a feed-back loop as part of the solution process