In this paper we re-formulate the automatic differentiation (and in particular, the backward automatic differentiation, also known as adjoint automatic differentiation, AAD) for random variables. While this is just a formal re-interpretation it allows one to investigate the algorithms in the presence of stochastic operators like expectation, conditional expectation or indicator functions.
We then specify the algorithms to efficiently incorporate non-pathwise operators (like conditional expectation operators). Under a comparably mild assumption it is possible to retain the simplicity of the backward automatic differentiation algorithm in the presence of conditional expectation operators. This simplifies important applications like - in mathematical finance - the application of backward automatic differentiation to the valuation of Bermudan options or calculation of xVA's.
We give the proof for a generalized version of the result. We then discuss in detail how the framework allows dramatic reduction of the memory requirements and improves the performance of a tapeless implementation of automatic differentiation (while the implementation brings advantages similar to ‘vector AAD’ (sometimes called tape compression) for free, it allows improvements beyond this. We present the implementation aspects and show how concepts from object-functional programing, like immutable objects and lazy evaluation enable additional reductions of the memory requirements. 相似文献
Two veins of literature, namely, production risk literature and stochastic frontier analysis, are examined. Both fields are concerned of output variation; the former due to exogenous shocks, the latter due inefficiency. By covering the literature from both the fields, this review suggests that the concept of heteroscedasticity can be utilized to build a synthesis between these mainly separate branches of literature. However, the synthetic approach brings a challenge how to differentiate between different sources of output variation. This challenge is identified as the main obstacle to meaningfully combine the two approaches. 相似文献
The examination of the intertemporal distribution of US productivity risk suggests that the conditional mean of productivity growth is an important determinant of macro quantities and asset prices. After establishing this empirical link, I rationalize it in a production economy featuring long-run productivity risk, Epstein and Zin (1989) preferences, and investment frictions. Both convex capital adjustment costs and convex reallocation costs across consumption and investment produce an annual equity premium as sizeable as in the data. 相似文献
It is agreed that agriculture provides avenues for impoverished households to produce and trade their way out of poverty. However, this requires market access and value chain integration of small-scale farmers. This paper explores the possibilities for integration of small-scale farmers into the mainstream commercial broiler value chain in South Africa. Production costs of small-scale producers are evaluated within the context of their commercial counterparts, with a case study approach. It revealed that small-scale producers pay more for inputs but also receive a substantial premium for sales of live birds in the informal market. This results in attractive gross margins for small-scale producers. There is, however, a production ceiling, due to demand and production considerations, associated with small-scale broiler production. This ultimately results in a dualistic industry with an informal (live sale) value chain at the one end of the spectrum and a sophisticated large-scale commercial value chain at the other. Given the salient production features and investment requirements associated with large-scale broiler production, organic growth from the small-scale value chain into the commercial value chain seems improbable. The dual nature of this industry should therefore be considered when developing policy geared towards development, poverty alleviation and value chain integration. 相似文献
This paper examines definitions of production boundaries in economics, explores the limitations of these definitions with respect to the inclusion of unpaid domestic labor, and considers the significance of such an exploration for feminist economic analysis. Margaret Reid's ''third party criterion,'' a definition of economic activity advocated by many feminists and one used to set the production boundary for most household production models, sets an implicit market standard for defining nonmarket economic activity and therefore contributes to the marginalization of such production. Similarly, production boundaries considered appropriate in third world contexts, such as those defined in the recently revised System of National Accounts, also use implicit market standards for defining nonmarket economic activity. A ''first world'' criterion implicit in such production boundaries defines nonmarket activity as work only if it would have been dealt with on the market in the first world; this results in the inclusion of some of the unpaid domestic activity of rural women on grounds which reinforce the exclusion of work such as child care and the preparation of meals in theory and policy. Feminist economists should beware the danger of recreating implicit assumptions and definitions which result in the exclusion of unpaid domestic labor. 相似文献
In this paper we investigate the firm-specific factors that account for the decision to invest in low-wage countries on the part of Italian firms in the textiles and clothing sector. This analysis is motivated by the fact that our survey data show, between 1990 and 1997, a decline of average employment in parent companies, while that in subsidiaries grew substantially. However, correlation and regression analysis show that employment in parent companies that invested in low-wage countries only seems to be negatively related with employment abroad. Our hypothesis is that investments in cheap labour countries are mainly cost-driven and are undertaken by firms that focus on a low-quality, low-cost strategy. We test this hypothesis through a probit analysis. The evidence suggests that investments to cheap labour countries are more likely to be of a vertical type, being relatively more labour-intensive compared with the parent company. Our hypothesis seems to be confirmed empirically. Investments in low-wage countries are more likely to generate abundant intra-firm trade and to be undertaken by firms with low shares of skilled employment. 相似文献