Optimal Insurance and Reinsurance Policies in the Risk Process

The paper examines a classical risk model where both insurance and reinsurance policies are chosen by the insurer in order to minimize the expected maximal loss. We show that the optimal control problem reduces to a static case. We found that the optimal reinsurance is excess of loss reinsurance and describe the set optimal insurance policies. Such a policy providing the minimal variance of the risk left with insured turns out to be a combination of stop loss and deductible policies. The results are illustrated by two numerical examples.

Optimal Insurance and Reinsurance Policies in the Risk Process

The paper examines a classical risk model where both insurance and reinsurance policies are chosen by the insurer in order to minimize the expected maximal loss. We show that the optimal control problem reduces to a static case. We found that the optimal reinsurance is excess of loss reinsurance and describe the set optimal insurance policies. Such a policy providing the minimal variance of the risk left with insured turns out to be a combination of stop loss and deductible policies. The results are illustrated by two numerical examples.

Removal of haem from lipids extracted from intact erythrocytes with particular reference to polyphosphoinositides

With the use of a modified acid version of a current lipid-extraction technique [Bligh & Dyer (1959) Can. J. Biochem. Physiol. 37, 911-917], 92% of phosphatidylinositol 4,5-bisphosphate obtained by means of three sequential extractions from intact human erythrocytes was obtained during the first one. Some 95% of the haem co-extracted with the lipids could then be removed, with a maximal loss of polyphosphoinositides of less than 3%. About 58 nmol of phosphatidylinositol 4,5-bisphosphate was found per ml of erythrocytes.

The Binding of Mercury by the Yeast Cell in Relation to Changes in Permeability

Yeast cells exposed to mercuric chloride suffer irreversible damage to the membrane, resulting in a loss of potassium and cellular anions to the medium. The maximal loss of K+, but not the time course of K+ loss is related to the mercury concentration, the relationship following a normal curve on a graph of log-concentration versus effect. It is concluded that the response is all or none for individual cells, and that with increasing concentrations of metal, the threshold is exceeded in an increasing proportion of the cells. Parallel studies of the binding of mercury by the cells indicate two distinct phases, only one of which is associated with the physiological response. The binding process is relatively slow but reaches an equilibrium state. Desorption is markedly dependent on temperature. No simple stoichiometric relationship exists between the binding of mercury and the physiological response (K+ loss).

An All-or-None Response in the Release of Potassium by Yeast Cells Treated with Methylene Blue and Other Basic Redox Dyes

Basic redox dyes, such as methylene blue, induce a loss of K+ from yeast cells. The maximal loss, rather than the rate of loss, is related to the dye concentration, the response following a normal distribution on a plot of log-dose, versus percentage loss of K+. This fact taken together with the observed correlation between K+ loss and frequency of staining (as measured by microscopic observation), indicates that the response is all-or-none for individual cells. The response is produced by all the basic redox dyes tested (9), but by none of the acidic dyes (4). However, only the oxidized form of the dye is effective. Cations protect the cells from the basic dyes in a competitive manner, the bivalent cations (especially UO2++) being more effective than monovalent cations. It is suggested that the action of the dyes involves two steps, the first a binding to ribonucleic acid in the cell membrane (with competition from cations) and the second, an oxidation of neighboring sulfhydryl groups to the disulfide form. At a threshold level, unique for each cell, a generalized membrane breakdown occurs, resulting in the release of potassium and of other cytoplasmic constituents.