Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast

2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.

A direct approach to the discounted penalty function

This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed-form expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48–78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773–1 784 (2010)], which uses different methods.

Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

Ruin problems under IBNR Dynamics

In this paper, we consider a discrete-time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg-type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non-delayed risk model, and numerical simulations are carried out with Belgian market data.

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Practice and Procedures - costs - offer to settle by plaintiff under UCPR r360 for amount of claim plus costs

In JLG Industries Inc v Teetree Pty Ltd [2002] QDC 031 the court considered the implications in terms of costs of an offer to settle by the plaintiff under the UCPR where the element of compromise involved only acceptance of the amount of claim without interest.

Estimating benefits of energy storage for aggregate storage applications in electricity distribution networks in Queensland

Electric Energy Storage (EES) is considered as one of the promising options for reducing the need for costly upgrades in distribution networks in Queensland (QLD). However, It is expected, the full potential for storage for distribution upgrade deferral cannot be fully realized due to high cost of EES. On the other hand, EES used for distribution deferral application can support a variety of complementary storage applications such as energy price arbitrage, time of use (TOU) energy cost reduction, wholesale electricity market ancillary services, and transmission upgrade deferral. Aggregation of benefits of these complementary storage applications would have the potential for increasing the amount of EES that may be financially attractive to defer distribution network augmentation in QLD. In this context, this paper analyzes distribution upgrade deferral, energy price arbitrage, TOU energy cost reduction, and integrated solar PV-storage benefits of EES devices in QLD.

Mechanism on flame retardancy of polystyrene/clay composites-The effect of surfactants and aggregate state of organoclay

Effects of organically modified montmorillonites (OMMTs) with different type and amount of modifiers on flame retardancy of polystyrene (PS) have been studied. The results from morphology analysis, gas chromatography-mass spectrometry and cone calorimeter have showed different mechanisms for the flame retardancy of PS/OMMTs composites, depending on surface property of OMNTrs. One is the catalysis of acid sites formed on the surface of octadecylammonium modified MMT (c-MMT) via Hoffman decomposition on the carbonization of degradation products, which promotes the formation of clay-enriched char barrier.

Mathematical modelling and optimisation of the formulation and manufacture of aggregate food products

In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.

Efficient aggregate computations in large-scale dense WSN

We focus on large-scale and dense deeply embedded systems where, due to the large amount of information generated by all nodes, even simple aggregate computations such as the minimum value (MIN) of the sensor readings become notoriously expensive to obtain. Recent research has exploited a dominance-based medium access control(MAC) protocol, the CAN bus, for computing aggregated quantities in wired systems. For example, MIN can be computed efficiently and an interpolation function which approximates sensor data in an area can be obtained efficiently as well. Dominance-based MAC protocols have recently been proposed for wireless channels and these protocols can be expected to be used for achieving highly scalable aggregate computations in wireless systems. But no experimental demonstration is currently available in the research literature. In this paper, we demonstrate that highly scalable aggregate computations in wireless networks are possible. We do so by (i) building a new wireless hardware platform with appropriate characteristics for making dominance-based MAC protocols efficient, (ii) implementing dominance-based MAC protocols on this platform, (iii) implementing distributed algorithms for aggregate computations (MIN, MAX, Interpolation) using the new implementation of the dominance-based MAC protocol and (iv) performing experiments to prove that such highly scalable aggregate computations in wireless networks are possible.

Recycling of glass cullet as aggregate for clays used to produce roof tiles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Do predators aggregate in response to pest density in agroecosystems? Assessing within-field spatial patterns

1. The spatial heterogeneity of predator populations is an important component of ecological theories pertaining to predator-prey dynamics. Most studies within agricultural fields show spatial correlation (positive or negative) between mean predator numbers and prey abundance across a whole field over time but generally ignore the within-field spatial dimension. We used explicit spatial mapping to determine if generalist predators aggregated within a soybean field, the size of these aggregations and if predator aggregation was associated with pest aggregation, plant damage and predation rate. 2. The study was conducted at Gatton in the Lockyer Valley, 90 km west of Brisbane, Australia. Intensive sampling grids were used to investigate within-field spatial patterns. The first row of each grid was located in a lucerne field (10 m from interface) and the remaining rows were in an adjacent soybean field. At each point on the grid the abundance of foliage-dwelling and ground-dwelling pests and predators was measured, predation rates [using sentinel Helicoverpa armigera (Hubner) egg cards] and plant damage were estimated. Eight grids were sampled across two summer cropping seasons (2000/01, 2001/02). 3. Predators exhibited strong spatial patterning with regions of high and low abundance and activity within what are considered to be uniform soybean fields. Ground-dwelling and foliage-dwelling predators were often aggregated in patches approximately 40 m across. 4. Lycosidae (wolf spiders) displayed aggregation and were consistently more abundant within the lucerne, with a decreasing trap catch with distance from the lucrene/soybean interface. This trend was consistent between subsequent grids in a single field and between fields. 5. The large amount of spatial variability in within-field arthropod abundance (pests and predators) and activity (egg predation and plant damage) indicates that whole field averages were misleading. This result has serious implications for sampling of arthropod abundance and pest management decision-making based on scouting data. 6. There was a great deal of temporal change in the significant spatial patterns observed within a field at each sampling time point during a single season. Predator and pest aggregations observed in these fields were generally not stable for the entire season. 7. Predator aggregation did not correlate consistently with pest aggregation, plant damage or predation rate. Spatial patterns in predator abundance were not associated consistently with any single parameter measured. The most consistent positive association was between foliage-dwelling predators and pests (significant in four of seven grids). Inferring associations between predators and prey based on an intensive one-off sampling grid is difficult, due to the temporal variability in the abundance of each group. 8. Synthesis and applications. This study demonstrated that generalist predator populations are rarely distributed randomly and field edges and adjacent crops can have an influence on within-field predator abundance. This must be considered when estimating arthropod (pest and predator) abundance from a set of samples taken at random locations within a field.

A beruházási projektek aggregált tőkeigénye = The Aggregate Capital Needs of Investment Projects

A tanulmány abból indul ki, hogy a beruházási projektek értékelése során egyidejűleg szükséges figyelembe venni a projektben lekötött tőkét és a lekötési időt mint jövedelemtermelési lehetőséget. Definiálja a projekt aggregált tőkeigényének fogalmát és megszerkeszti a vonatkozó mérőszámot. Az aggregált tőkeigény új vállalatgazdasági kategória, mely a beruházási projektek értékelésének egy új megközelítését teszi lehetővé. A projekt aggregált tőkeigénye azt a tőkeösszeget jelenti, mely a projekt működtetéséhez annak teljes élettartama alatt szükséges. A három meghatározó tényező: a kezdőtőke, a megtérülési idő (illetőleg az élettartam) és a megtérülés gyorsasága. A számszerűsítéshez minden évre vonatkozóan meg kell határozni az adott évben lekötött tőkét, ami az adott évig még meg nem térült tőkerészt jelenti, majd ezek összegzése révén adódik az aggregált tőkeigény. A mértékegység egységnyi tőke egyévi lekötése. A tanulmány az összefüggések modellszerű levezetése mellett gazdag példaanyagot is tartalmaz. Az elemzés bővíti a nettó jelenérték tartalmára vonatkozó ismereteket, rávilágít az aggregált tőkeigény ismeretének fontosságára mind a nettó jelenérték, mind a belső kamatláb esetében. _____ The starting point of this paper is that in the evaluation process of investment projects necessary to take into account simultaneously the tied-up capital and tiedup time as the income-generating potential. For this, it defines a special content of aggregate capital needs of investment projects, and elaborates an index. The aggregate capital needs is a new business economics category, which provides a new aspect to evaluate investment projects. This means the amount of capital needed for the operation of the project during its full duration. Three factors determine the aggregate capital needs for investments projects. These are the amount of initial investment, the payback period (or the duration) and the rapidity of capital payback. The solution is to sum up the yearly tied-up capital, that is, the notreturned parts of the capital for each year. The measurement unit is one unit tied-up capital for one year. The paper formulates the main relationships as models and by way of explanation presents some examples. The analysis highlights the importance of considering the aggregate capital needs furthermore widens knowledge regarding the net present value and internal rate of return.