Essays on the treatment of cash flows under stochastic interest rates

Abstract This paper shows how to calculate recursively the moments of the accumulated and discounted value of cash flows when the instantaneous rates of return follow a conditional ARMA process with normally distributed innovations. We investigate various moment based approaches to approximate the distribution of the accumulated value of cash flows and we assess their performance through stochastic Monte-Carlo simulations. We discuss the potential use in insurance and especially in the context of Asset-Liability Management of pension funds.

Dynamic drag modeling of submerged aquatic vegetation canopy flows

Vegetation has a profound effect on flow and sediment transport processes in natural rivers, by increasing both skin friction and form drag. The increase in drag introduces a drag discontinuity between the in-canopy flow and the flow above, which leads to the development of an inflection point in the velocity profile, resembling a free shear layer. Therefore, drag acts as the primary driver for the entire canopy system. Most current numerical hydraulic models which incorporate vegetation rely either on simple, static plant forms, or canopy-scaled drag terms. However, it is suggested that these are insufficient as vegetation canopies represent complex, dynamic, porous blockages within the flow, which are subject to spatially and temporally dynamic drag forces. Here we present a dynamic drag methodology within a CFD framework. Preliminary results for a benchmark cylinder case highlight the accuracy of the method, and suggest its applicability to more complex cases.

Ecosystem impacts of Alpine water intakes for hydropower: the challenge of sediment management

The natural flow hydrological characteristics (such as the magnitude, frequency, duration, timing, and rate of change of discharge) of Alpine streams, dominated by snowmelt and glacier melt, have been established for many years. More recently, the ecosystems that they sustain have been described and explained. However, natural Alpine flow regimes may be strongly modified by hydroelectric power production, which impacts upon both river discharge and sediment transfer, and hence on downstream flora and fauna. The impacts of barrages or dams have been well studied. However, there is a second type of flow regulation, associated with flow abstraction at intakes where the water is transferred laterally, either to another valley for storage, or at altitude within the same valley for eventual release downstream. Like barrages, such intakes also trap sediment, but because they are much smaller, they fill more frequently and so need to be flushed regularly. Downstream, while the flow regime is substantially modified, the delivery of sediment (notably coarser fractions) remains. The ecosystem impacts of such systems have been rarely considered. Through reviewing the state of our knowledge of Alpine ecosystems, we outline the key research questions that will need to be addressed in order to modify intake management so as to reduce downstream ecological impacts. Simply redesigning river flows to address sediment management will be ineffective because such redesign cannot restore a natural sediment regime and other approaches are likely to be required if stream ecology in such systems is to be improved.