Thesis: Sc. D., Massachusetts Institute of Technology, Department of Civil Engineering, 1975 / Vita. / Bibliography: leaves 213-221. / Sc. D. / Sc. D. Massachusetts Institute of Technology, Department of Civil Engineering

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published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

The three dimensional distribution of clouds is of great interest to the Air Force, and to the aviation community in general. The Stochastic Cloud Forecast Model (SCFM) is a novel, global cloud model currently operated at the Air Force Weather Agency (AFWA) which diagnoses cloud cover statistically using a minimal set of predictors from global numerical forecasts. Currently the four predictors are pressure, temperature, vertical velocity, and relative humidity. In this thesis, 330 sets of predictors are compared in the SCFM-R, a research version of the model programmed for this thesis. There are some differences in the SCFM and the SCFM-R that yield important information. It is found that the SCFM is very sensitive to how cloud cover in the boundary layer is diagnosed. An analysis of the diagnosis method used to initialize the model revealed a bias for over-diagnosing cloud at lower levels and under-diagnosing cloud at upper levels. Also, it is recommended that AFWA consider exchanging temperature for another predictor more related to moisture, such as cloud water, and that relative humidity is included as relative humidity to the fourth power. Other recommendations include improving the method for diagnosing cloud cover in the boundary layer and improving the model initial condition.

This thesis describes an inventory-theoretic approach to the study of the demand for money. It aims to connect money demand theory with optimal inventory theory on the one hand and with time series empirical evidence on the other. Thus it incorporates recent advances in inventory theory and extends these to allow the interest rate to follow a stochastic process. The problem of minimising the expected, discounted suns of cash-management costs is ascribed to an agent. Through the use of continuous-time, stochastic, optimal control an optimal cash-management policy is shown to exist and be of a familiar target-threshold form. Closed-form expressions for the forward-looking time-varying targets and thresholds are derived in special cases. The steady-state, Baumol-Tabin model, a further special case, also is examined in detail. The theory implies that expected future interest rates may influence money holdings despite the absence of strictly convex adjustment costs. A distributed-1ag expression for these holdings is proposed in which the adjustment and expectations dynamics are derived front theory. Aggregation over time and, to a lesser extent, over agents is treated explicitly. The econometric issues involved in testing models of the demand for money with rational expectations are outlined and simulation evidence on the predictions of the theory is provided. The theory gives rise to new predictions concerning expectations effects and variable adjustment speeds. It can also account for the findings of empirical research. In particular, it largely resolves the problem of slow adjustment in empirical money demand equations.

Ph. D, Faculty of Science, University of Witwatersrand, 2011 / Research in the area of stochastic models for actuarial use in South Africa is limited to relatively few publications. Until recently, there has been little focus on actuarial stochastic models that describe the empirical stochastic behaviour of South African financial and economic variables. A notable exception is Thomson’s (1996) proposed methodology and model. This thesis presents a collection of five papers that were presented at conferences or submitted for peer review in the South African Actuarial Journal between 1996 and 2006. References to subsequent publications in the field are also provided. Such research has implications for medium and long-term financial simulations, capital adequacy, resilience reserving and asset allocation benchmarks as well as for the immunization of short-term interest rate risk, for investment policy determination and the general quantification and management of risk pertaining to those assets and liabilities. This thesis reviews Thomson’s model and methodology from both a statistical and economic perspective, and identifies various problems and limitations in that approach. New stochastic models for actuarial use in South Africa are proposed that improve the asset and liability modelling process and risk quantification. In particular, a new Multiple Markov-Switching (MMS) model framework is presented for modelling South African assets and liabilities, together with an optimal immunization framework for nominal liability cash flows. The MMS model is a descriptive model with structural features and parameter estimates based on historical data. However, it also incorporates theoretical aspects in its design, thereby providing a balance between purely theoretical models and those based only on empirical considerations.