The optimal dividend barrier in the Gamma-Omega model

In the traditional actuarial risk model, if the surplus is negative, the company is ruined and has to go out of business. In this paper we distinguish between ruin (negative surplus) and bankruptcy (going out of business), where the probability of bankruptcy is a function of the level of negative surplus. The idea for this notion of bankruptcy comes from the observation that in some industries, companies can continue doing business even though they are technically ruined. Assuming that dividends can only be paid with a certain probability at each point of time, we derive closed-form formulas for the expected discounted dividends until bankruptcy under a barrier strategy. Subsequently, the optimal barrier is determined, and several explicit identities for the optimal value are found. The surplus process of the company is modeled by a Wiener process (Brownian motion).

The epidthelial sodium channel ENaC and its regulators in the epidermal permeability barrier function

The highly amiloride-sensitive epithelial sodium channel ENaC is well known to be involved in controlling whole body sodium homeostasis and lung liquid clearance. ENaC expression has also been detected in the skin of amphibians and mammals. Mice lacking ENaC expression lose rapidly weight associated with an epidermal barrier defect that develops following birth. This dehydration is accompanied with a highly abnormal lipid matrix composition and an impaired skin surface acidification. This strongly suggests a role of ENaC in the maturation of barrier function rather than in the prenatal generation of the barrier, and may be as such an important modulator for skin hydration. In parallel, gene targeting experiments of regulators of ENaC activity, membrane serine proteases, also termed channel activating proteases, like CAP1/Prss8 and matriptase/MT-SP1 by themselves have been shown to be crucial for the epidermal barrier function. In our review, we mainly focus on the role of ENaC and its regulators in the skin and discuss their importance in the epidermal permeability barrier function.