Finite element approximation of source term identification with TV-regularization

In this paper we investigate the problem of recovering the source term in an elliptic system from a measurement of the state on a part of the boundary. For the particular interest in reconstructing probably discontinuous sources, we use the standard least squares method with the total variation regularization. The finite element method is then applied to discretize the minimization problem, we show the stability and the convergence of this technique. Furthermore, we have proposed an algorithm to stably solve the minimization problem. We prove the iterate sequence generated by the derived algorithm converging to a minimizer of the regularization problem, and that convergence measurement is also established. Finally, a numerical experiment is presented to illustrate our theoretical findings.Comment: Inverse source problem, boundary observation, total variation regularization, ill-posedness, finite element method, stability and convergence, elliptic boundary value proble

A reaction coefficient identification problem for fractional diffusion

We analyze a reaction coefficient identification problem for the spectral fractional powers of a symmetric, coercive, linear, elliptic, second-order operator in a bounded domain $\Omega$. We realize fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on the semi-infinite cylinder $\Omega \times (0,\infty)$. We thus consider an equivalent coefficient identification problem, where the coefficient to be identified appears explicitly. We derive existence of local solutions, optimality conditions, regularity estimates, and a rapid decay of solutions on the extended domain $(0,\infty)$. The latter property suggests a truncation that is suitable for numerical approximation. We thus propose and analyze a fully discrete scheme that discretizes the set of admissible coefficients with piecewise constant functions. The discretization of the state equation relies on the tensorization of a first-degree FEM in $\Omega$ with a suitable $hp$-FEM in the extended dimension. We derive convergence results and obtain, under the assumption that in neighborhood of a local solution the second derivative of the reduced cost functional is coercive, a priori error estimates

Moments of the generalized hyperbolic distribution

In this paper we demonstrate a recursive method for obtaining the moments of the generalized hyperbolic distribution. The method is readily programmable for numerical evaluation of moments. For low order moments we also give an alternative derivation of the moments of the generalized hyperbolic distribution. The expressions given for these moments may be used to obtain moments for special cases such as the hyperbolic and normal inverse Gaussian distributions. Moments for limiting cases such as the skew hyperbolic t and variance gamma distributions can be found using the same approach.Generalized hyperbolic distribution; hyperbolic distribution; kurtosis; moments; normal inverse Gaussian distribution; skewed-t distribution; skewness; Student-t distribution.

SME Access to Credit

The aim of this paper is to inform the reader about the access to credit of small and medium sized enterprises (SMEs) in Vietnam based on two SME surveys. Recent evidence from a variety of sources suggests that credit to available to SMEs has increased over the past few years. This is confirmed by the two SME surveys. Fewer firms which applied for credit in 2005 were denied credit as compared to 2002. However, the rapid development of the private sector has also increased demand for credit (especially among the larger SMEs); and it appears that the formal financial sector is just managing to keep track with growth in general. We conclude by discussing these results and formulate a set of policy recommendations.Vietnam; credit constraints; financial markets

SME Fringe Benefits Provision

The aim of this paper is to inform the reader about the distribution of fringe benefits provided to employees by firms in 10 provinces of Vietnam. Five types of benefits are considered: Annual leave, maternity leave, sick leave, social insurance and health insurance. We especially focus on whether the gender of the owner has an effect on the fringe benefits provided. It appears that women firm owners are more likely to provide employees with fringes, and this gender effect exists primarily in non-household enterprises and is robust to the inclusion of standard determinants of wage compensation. We dscuss these results and formulate a set ofpolicy recommendations.Vietnam; gender; fringe benefits

Testing for Food market integration: A study of the Vietnamese paddy market

With its increasing integration into the world economy, agricultural exports and rural incomes in Vietnam have increased substantially in recent years. At the sub-national level, however, there are concerns that not all regions and categories of agricultural producers have and will benefit from the ongoing liberalization of agricultural markets. Vietnam's elongated geography and lack of spatial market integration pose special problems in this regard. Accordingly, this study aims to answer three interrelated questions: (a) whether there is spatial integration between paddy markets in the North and South of Vietnam; (b) whether there is spatial integration in paddy markets within the North and within the South; and, (c) if within-region integration is stronger and faster than between-region integration. The empirical model we develop to answer these questions, uses estimates of transfer costs to generalize the well known model of spatial market integration due to Ravallion to allow for the possibility of threshold effects. A sequential testing strategy is developed which progressively tests for market segmentation, the number of thresholds, long-run market integration, common dynamics/informational efficiency, and (a strict version of) the 'Law' of One Price within an error-correction framework. When the unrestricted version of this model is estimated using monthly paddy prices for eight markets between 1993 and 2006, we find weak evidence of market integration between paddy markets in the North and South of Vietnam with an absence of threshold effects. However, there is evidence of both threshold effects and stronger forms of spatial market integration for paddy markets within the North and within the South, with at least 60% percent of price changes being transmitted between markets within one month whenever price spreads exceeds their upper or lower thresholds. The extent and speed of price transmission within regional paddy markets is generally faster in the South than the North of Vietnam. However, the instantaneous version of the 'Law' of One Price, which requires full price adjustment to occur within a month, only holds for a few regimes and market pairs. Three main policy implications flow from these results. First, since there is limited evidence of integration between paddy markets in the North and South of Vietnam, national level policies cannot be relied upon to stabilize or support paddy prices.Second, since there is evidence of spatial market integration within the Red River and Mekong River deltas, paddy markets within these regions can be relied upon to transmit price signals between deficit and surplus areas relatively well. Third, since the speed and extent of price transmission is relatively rapid within the North and within the South of Vietnam, the private sector trade can be relied upon to transfer rice and paddy between markets in an efficient manner. Problems might, however, emerge if large demand-supply imbalances were to emerge between the North and South, as transfer costs would prevent private sector trade taking place. In these circumstances, the public sector might need to intervene, in a consistent and market friendly way, to ensure adequate food supplies in the short-term.Market integration; Paddy market; Error-correction; Spatial integration; Vietnam