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A multivariate stochastic approach to determine long-term success of SA living annuity portfolios
(Actuarial Society of South Africa, 2025) Van Niekerk, Andries Jacobus; Moutzouris, Vasili; Mare, Eben; vanniekerk.dries@tuks.co.za
Success rates of living annuities within the South African retirement landscape are examined through portfolio modelling that includes domestic equities, cash, and international exposure, via the S&P 500 index. We define success rates based on Cooley’s framework, emphasising financial sustainability throughout retirement. Our approach incorporates foreign exposure by converting S&P 500 gains to South African Rand, accounting for stochastic foreign exchange rate fluctuations. Additionally, US and South African inflation rates are integrated to assess success rates in real terms, ensuring the impact of inflation on retirees’ income is accurately captured. This study incorporates stochastic correlation and stochastic volatility modelling to capture dynamic asset relationships under varied market conditions. The S&P 500 and JSE Top 40 equities are modelled with stochastic volatility, calibrated through the Efficient Method of Moments (EMM), enhancing volatility estimation for equity assets. These techniques support the analysis of optimal portfolio compositions and withdrawal strategies to maximise annuity success rates, providing evidence-based insights for retirement planning in South Africa.
Leave-group-out cross-validation for latent Gaussian models
(Institut d'Estadistica de Catalunya, 2025-07-04) Liu, Zhedong; Van Niekerk, Janet; Rue, Håvard
Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations, LOOCV has since been extended to other cases such as hierarchical models. However, it focuses rimarily on short-range prediction and may not fully capture long-range prediction scenarios. For structured hierarchical models, particularly those involving multiple random effects, the concepts of short- and long-range predictions become less clear, which can complicate the interpretation of LOOCV results. In this paper, we propose a complementary cross-validation framework specifically tailored for longer-range prediction in latent Gaussian models, including those with structured random effects. Our approach differs from LOOCV by excluding a carefully constructed set from the training set, which better emulates longer-range prediction conditions. Furthermore, we achieve computational efficiency by adjusting the full joint posterior for this modified cross-validation, thus eliminating the need for model refitting. This method is implemented in the R-INLA package (www.r-inla.org) and can be adapted to a variety of inferential frameworks.
Crystallisation and petrogenesis of cenozoic alkaline basaltic lavas on the Kapsiki Plateau (Moukoulvi, Far-North Cameroon) : unveiling the mantle's heterogeneity and HIMU signature
(Elsevier, 2025-06) Djamilatou, Diddi Hamadjoda; Dedzo, Merlin Gountie; Lenhardt, Nils; Tsozue, Desire; Nkengmatia, Elvis Asaah Asobo; Ngarena, Moussa Klamadji
The Kapsiki Plateau represents the northernmost extension of the Cameroon Volcanic Line (CVL) in West Africa. Unlike other regions of the CVL, this area is characterised by a higher prevalence of felsic and intermediate rocks compared to basaltic ones. Detailed investigations into the petrogenetic evolution of these rocks are currently limited. For this reason, Cenozoic alkaline basaltic lavas from the Kapsiki Plateau (Moukoulvi) were studied to enhance comprehension of their crystallisation process, genetic evolution of the magma, and insights into its petrogenesis and source mineralogy. The examined lavas are comparable to the mafic lavas that span the whole range of the CVL and demonstrate major and trace element characteristics similar to those seen in ocean island basalts (OIB). The major and trace element compositions suggest fractional crystallisation mainly including olivine, clinopyroxene, and Fe–Ti oxide with evidence of crustal contamination. The multi-element diagrams reveal consistency with those reported from other CVL volcanoes, displaying depletion of heavy rare earth elements (HREE) and enrichment of light rare elements (LREE), indicating an enriched source and the existence of garnet. The studied lavas have high large ion lithophile element (LILE) contents (Sr = 812–1065 ppm, Ba = 394–467 ppm) relative to high field strength elements (HFSE) (Sr/Zr = 3.97–4.94; average OIB = ∼1 Ba/La = 9.42–11.72; average OIB = 9.4). They also have Zr/Sm ratios (26.93–29.88) that are similar to the average OIB (Zr/Sm = 28). Moreover, the studied lavas exhibit elevated levels of incompatible trace elements (e.g., Rb, Pr, U, and Th), as well as higher Ta/Yb and Th/Yb ratios compared to normal OIB values, associated with a notable fluctuation in Nb/Ta and Zr/Hf ratios. The correlations between Th, La, U, and SiO2, coupled with the trend of the samples on Nb/Y vs. Rb/Y diagrams, indicate the influence of crustal contamination on the lavas' composition. The source of these lavas was a heterogeneous source with less than 4 % garnet that underwent partial melting of less than 2 %. The presence of a Pb depletion (Ce/Pb > 30) also implies that these magmas belong to the high μ (HIMU)-OIB type, attributed to lithospheric mantle metasomatism. The formation of these magmas involved partial melting of a mantle source evolving chemically and mineralogically over time with a HIMU composition at very low temperatures. Hydrous minerals, such as phlogopite or amphibole, may indicate modal metasomatism, supported by high Rb/Sr ratios or K2O high levels. Sr/Zr ratios (3.97–4.94) above OIB values (0.8–1.5) suggest Sr and Ba-rich fluid influence. Elevated Zr/Sm ratios (>28) and variations in Nb/Ta and Zr/Hf ratios point to metasomatic fluids or melts altering the mantle's composition. Therefore, the Moukoulvi lavas, like many CVL alkaline lavas, likely erupted from a metasomatized mantle source that was enriched in incompatible trace elements (Rb, Ba, Ce, Nb, and Zr). This enrichment is reflected in the elevated concentrations of these incompatible trace elements, as well as the relative enrichment in HFSE. The absence of temperature anomalies in the upper mantle beneath the CVL suggests that the magmatism originates from the lithospheric mantle source rather than a mantle plume.
The influence of applying a solar dish to parallel-flow configurations of a Brayton cycle
(Elsevier, 2025-03) Cockcroft, C.C.; Le Roux, Willem Gabriel; willem.leroux@up.ac.za
When adding additional pressure loss components to a Brayton cycle, parallel-flow cycles can be a viable alternative for single-shaft and twin-shaft gas turbines. This study seeks to investigate how a solar heat input, captured via a solar dish and open-cavity tubular receiver, influences various simple and recuperated parallel-flow cycle configurations. Two solar receiver placements are considered: before the combustor, and before the power turbine (which is in parallel with the cycle). Various power turbine split-off points are considered: after the compressor, after the recuperator, after the solar receiver and after the combustor. In this work, various novel solar-dish parallel-flow Brayton cycles that make use of combinations of commercial radial turbochargers to form microturbine configurations are therefore investigated. The best-performing main shaft turbocharger, the G25-550 (AR = 0.92), was selected for analysis together with the GBC14-200 or the GBC17-250 as the power turbine. Variable recuperator dimensions were also introduced to obtain maximum fuel-based thermal efficiencies while remaining within, or as close as possible to, the maximum allowable gasifier turbine inlet temperatures. For unrecuperated cycles, the cycle with the solar receiver placed before the combustor and the power turbine split-off point directly after the combustor provided the best fuel-based thermal efficiency of 7 % at a pressure ratio of 2.75 (with 14.5 kW power output). For recuperated cycles, the cycle with a split-off point directly after the compressor, flowing to both the solar receiver and power turbine, achieved the highest fuel-based thermal efficiency of 22 % at a pressure ratio of 1.5 (with 3 kW power output).
An investigation into the feasibility of using virtual environments as an induction method in SHIP® therapy
(South African Computer Society, 2025-06) Malan, Adolf Weich; Bosman, Isak de Villiers; Bothma, T.J.D. (Theodorus Jan Daniel); isak.bosman@up.ac.za
Virtual reality contributes to the successful treatment of patients by assisting those who have difficulty with the process of imagining the required visual images needed during psychotherapy. SHIP® is a form of psychotherapy that suggests that spontaneous healing is a natural tendency that emerges from within a person. It identifies certain activator images as essential pathways for accessing unconscious trauma material that needs healing. The purpose of this study was to examine whether virtual reality can be used as a medium to induce memories through the utilisation of neutral images based on the SHIP® Frame. Two groups of participants were gathered: one group underwent a traditional SHIP® session while the other group underwent the virtual induction with the aid of a head mounted display. A random clinical trial was used to determine the level of induction and identify the helpful aspects that contributed to the induction. The results indicated that virtual reality was able to assist as a cognitive stimulus as well as a cognitive proxy in the overall process of SHIP®.