Resource allocation

This report discusses the problem of the allocation of resources: how should an organisation (such as MOD) invest bearing in mind the long term delay for the realization of investment strategies, and how might this apply in times of increasing budgetary constraints? After making certain simplifying assumptions, the Study Group constructed a prototype model based on the method of Optimal Control. This allows the decision maker to investigate the impact of particular investment strategies over a period of years, the impact being measured in terms of “quality” or “capability”. Interventions can be designed so that “quality” (Q) is maximized at a particular time, or so that the average quality over a given time interval is maximized. Both of these approaches are explored. This model shows reasonable behaviour when tested over a parameter set. It could be used as part of a systems approach to the defence budget as a whole, but the method itself is scalable to smaller (or larger) resourcing conundrums

In-Situ Thermal Remediation of Contaminated Soil

Recently, a method for removing contaminants from soil (several meters under the ground) has been proposed by McMillan-McGee Corp. The process can be described as follows. Over a period of several weeks, electrical energy is introduced to the contaminated soil using a multitude of finite length cylindrical electrodes. Current is forced to flow through the soil by the voltage differentials at the electrodes. Water is also pumped into the soil via the injection well and out of the ground at the extraction well. The soil is heated up by the electrical current and the contaminated liquids and vapours are produced at the extraction well. The temperature of the contaminated soil, during the process, is believed to reach the maximum value (the boiling temperature of water). Normally, the electrodes are placed around the contaminated site and the extraction well is located in the centre of the contaminated region. The distance between the electrodes is usually seven to eight meters. The distance between the extraction well and an electrode is about four meters. The diameter of the electrodes is 0.2 meter and the extraction well is 0.1 meter in diameter. The reason for using the electrical current is that “flushing” the soil using water alone is not effective for removing the contaminants. By heating up the soil and vaporizing the contaminated liquid, it is anticipated that rate of extraction will increase as long as the recondensation is not significant. A major concern, therefore, is whether recondensation will occur. Intuitively, one might speculate that liquid phase may dominate near the injection well. Moving away from the injection site towards the extraction well, due to the combined effects of lower pressure and higher temperature (from heating), phase change occurs and a mixture of vapour and liquid may co-exist. There may also be a vapour-only region, depending on the values of temperature, pressure, and other parameters. In the two-phase zone, since vapour bubbles tend to rise due to the buoyancy force, and the temperature decreases along the vertical path of the bubbles out of the heated region, it is possible that the bubbles will recondense before reaching the extraction well. As a consequence, the probability exists that part of the contaminants stay in the soil. Obviously, to predict transition between single-phase and two-phase regions and to understand the transport phenomenon in detail, a thermal capillary two-phase flow model is needed. However, to simplify the problem, here we only consider the case when two-phases co-exist in the entire region

Valuation and hedging of the ruin-contingent life annuity (RCLA)

This paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income per year for life, akin to a defined benefit pension, but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters. The motivation for studying the RCLA on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately \$1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. Second, the U.S. administration - both Treasury and Department of Labor - have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job