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

Yield Measures for Special-Interest Australian Inbound Tourism Markets

Different tourism stakeholders mean different things by ‘yield’ and this presents a barrier to communication and policy discussion. Primarily, this paper provides an overview of different concepts of yield. It also operationalizes several of these measures using inbound tourism expenditure data for Australia so that the origin markets and market segments identified as generating high yields under the various measures can be compared. The paper further identifies the manner in which the concept of yield can be broadened to embrace sustainable yield by incorporating measures of environmental and social impact. It concludes with a discussion of the policy implications of the study