(First of Two Parts) IN recent years, there has been a substantial increase in the application of mathematical modeling and dynamic systems analysis to quantitative studies of metabolic pathways. Such technics, when applied by those who fully appreciate their merits and limitations, are important investigative tools. To obtain the optimal amount of useful information, there is a need for close collaboration between workers in the different disciplines involved. Adoption of inappropriate models or mathematical technics can lead to results that, at best, fail to make full use of the available data but more often are physiologically implausible. This review outlines . . .

Use of kinetic analysis and mathematical modeling in the study of metabolic pathways in vivo. Applications to hepatic organic anion metabolism. (First of two parts).

In recent times the Australian insurance market, particularly the Liability section of it, has been characterized by violent changes in premium rate. For a number of years premium rates declined to a point where the market, on average, was underwriting at a considerable loss. This trend was reversed by a sequence of large increases in premium rates to the point where, on average, substantial profits were probably being made. During these fluctuations in premium rates the various operators in the market appeared to act in a similar manner; generally, these individual operators followed ‘the market’ as its average premium rates declined and then increased. From the viewpoint of rational product pricing, this cyclical behaviour of premium rates is peculiar. It raises questions as to 1. what ‘the market’ was attempting to achieve by such pricing; 2. what individual insurers were attempting to achieve in following the market. The present paper investigates the appropriate response of an individual insurer to movements in market premium rates. It is assumed that the management objective of this insurer is maximization of expected discounted profit arising between the present and some planning horizon. Price-elasticity of demand for the insurance produce is taken into account. Section 5 provides an explicit formula for the response of optimal pricing policy to changes in market premium rates. Several theorems are developed there indicating the response of this optimal policy to changes in various parameters. The same section provides a verbal interpretation of those theorems. It is found that optimal strategies do not follow what might be thought the obvious rules. In particular, it is not the case that profitability is best served by following the market during a period of premium rate depression. The relation between the market's behaviour and optimal response of an individual insurer is a complex one. It depends upon various factors, including 1. the predicted time which will elapse before a return of market rates to profitability; 2. the price-elasticity of demand for the insurance product under consideration; 3. the rate of return required on the capital supporting the insurance operation. Each of these features is illustrated in the numerical examples of Section 7. In particular, it is seen that the optimal strategy may well involve underwriting for significant profit margins at times when the average market premium rate is well short of breaking even. On the other hand, conditions can arise in which the optimal premium rating strategy will indicate loss leading in the near future. As a very broad generalization, this may be the case when the current average market rate lies below the break-even rate, but is expected to return to substantial profitability in the very near future. The phrases ‘substantial profitability’ and ‘very near future’ are both operative in this generalization (see Section 7.5). One of the numerical examples demonstrates that optimal strategies will not involve loss leaders, irrespective of the degree of competition from the market, if the demand function for the insurance product assumes certain forms. These particular forms are not unrealistic. It follows that some market research on the shape of the demand function may assist an insurer seeking to determine a suitable underwriting strategy. In fact, some sections toward the end of the paper point out that there are other factors, and particularly taxation considerations (Section 9.1), which need to be considered before an optimal strategy involving loss leading be adopted. Again as a broad generalization, it may be said that these considerations tend to militate against loss leading. In summary then, it appears that the longer term profitability of an insurer will only comparatively rarely be best served by underwriting for deliberate losses. Section 10 gives details of a small survey of Australian underwriters. These underwriters have stated the manner in which they would respond, in terms of pitching their rates, to a particular set of circumstances in a competitive market. These responses are compared with the optimal response.

Underwriting strategy in a competitive insurance environment

The paper proposes a model of strain resistance of alloy under high-temperature deformation. The model describes hardening of alloy due to the increase of dislocation density, as well as the barrier effect of blocking free dislocations, boundaries of grains and subgrains by dispersoids. The model also takes into account the softening processes associated with the recovery and dynamic recrystallization. The model has been tested on the rheological behavior of an Al-Mg alloy named AMg6 at temperatures of 400 and 500 oC in the range of strain rates from 5 to 25 s. It was found in this temperature – strain rate range that the curve of strain resistance of the AMg6 alloy consists of several portions. First there is hardening of the material, then there is material softening, which is again replaced by hardening of the material. With the use of the electron backscatter diffraction technique and transmission electron microscopy, it was found that the main process of softening at investigated temperatures is dynamic recrystallization. The appearance of the second portion of hardening on the strain resistance curve is the inhibition of dynamic recrystallization, as well as manifestation of the barrier effect of blocking free dislocations, grain and subgrain boundaries by dispersoids.

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Modelling and Simulation of Strain Resistance of Alloys Taking into Account Barrier Effects

Investigations of a relatively new magnetic levitation device are described. This device uses an electromagnet, which is the inductive part of a resonant circuit. If the circuit is properly tuned, static stability is attainable. In order to understand the dynamic instabilities and to enable systematic design of tuned circuit levitators. a method is needed, which permits rapid analysis. In the models investigated, the frequency of supply is much higher than that associated with the mechanical vibrations, and as a result, a direct digital simulation of the equations is inefficient. This difficulty is overcome by using an approximation of slowly varying quantities. Due to the omission of the detailed high frequency oscillation from this new representation, it has been found possible to obtain a solution of an example by using only a few steps of integration. The results agree with those observed in an experimental model. They also agree with analogue simulations.

Reginald F. Brown

Papers

Control Theory: Identification and Optimal Control