An Analogue of the Cramér–Lundberg Approximation in the Optimal Investment Case

We consider ruin probabilities for an insurance company, which can also invest in the stock market. The risk process is modeled by a compound Poisson process and the stock price by geometric Brownian motion. We show that if the tails of the claims are light tailed, then the optimal strategy is asymptotically given by holding a constant $-value in the stock position. Furthermore, we show that a kind of Cramér–Lundberg approximation holds for the minimal ruin probability. Everything is shown under assumptions, which are analogous to the assumptions in the case of the classical Cramér–Lundberg approximation without investment.     

Risk averse asymptotics in a Black–Scholes market on a finite time horizon

We consider the optimal investment and consumption problem in a Black–Scholes market, if the target functional is given by expected discounted utility of consumption plus expected discounted utility of terminal wealth. We investigate the behaviour of the optimal strategies, if the relative risk aversion tends to infinity. It turns out that the limiting strategies are: do not invest at all in the stock market and keep the rate of consumption constant!     

Some notes on Sonine–Gegenbauer integrals

We provide an explicit formula for a Sonine–Gegenbauer integral, which seems to be unknown in the literature so far. For another type of these integrals, we show a dependence relation over the rational functions, including the explicit calculation of the coefficient functions.     

Optimal Consumption in a Brownian Model with Absorption and Finite Time Horizon

We construct ?-optimal strategies for the following control problem: Maximize $\mathbb {E}[ \int_{[0,\tau)}e^{-\beta s}\,dC_{s}+e^{-\beta\tau}X_{\tau}]$ , where X _t =x+μt+σW _t ?C _t , τ≡inf{t>0|X _t =0}∧T, T>0 is a fixed finite time horizon, W _t is standard Brownian motion, μ, σ are constants, and C _t describes accumulated consumption until time t. It is shown that ?-optimal strategies are given by barrier strategies with time-dependent barriers.     

Optimal Consumption Under Deterministic Income

We consider an individual or household endowed with an initial wealth, having an income and consuming goods and services. The wealth development rate is assumed to be a deterministic continuous function of time. The objective is to maximize the discounted consumption over a finite time horizon. Via the Hamilton–Jacobi–Bellman approach, we prove the existence and the uniqueness of the solution to the considered problem in the viscosity sense. Furthermore, we derive an algorithm for explicit calculation of the value function and optimal strategy. It turns out that the value function is in general not continuous. The method is illustrated by two examples.     

Structure based classification for bile salt export pump (BSEP) inhibitors using comparative structural modeling of human BSEP

The bile salt export pump (BSEP) actively transports conjugated monovalent bile acids from the hepatocytes into the bile. This facilitates the formation of micelles and promotes digestion and absorption of dietary fat. Inhibition of BSEP leads to decreased bile flow and accumulation of cytotoxic bile salts in the liver. A number of compounds have been identified to interact with BSEP, which results in drug-induced cholestasis or liver injury. Therefore, in silico approaches for flagging compounds as potential BSEP inhibitors would be of high value in the early stage of the drug discovery pipeline. Up to now, due to the lack of a high-resolution X-ray structure of BSEP, in silico based identification of BSEP inhibitors focused on ligand-based approaches. In this study, we provide a homology model for BSEP, developed using the corrected mouse P-glycoprotein structure (PDB ID: 4M1M). Subsequently, the model was used for docking-based classification of a set of 1212 compounds (405 BSEP inhibitors, 807 non-inhibitors). Using the scoring function ChemScore, a prediction accuracy of 81% on the training set and 73% on two external test sets could be obtained. In addition, the applicability domain of the models was assessed based on Euclidean distance. Further, analysis of the protein–ligand interaction fingerprints revealed certain functional group-amino acid residue interactions that could play a key role for ligand binding. Though ligand-based models, due to their high speed and accuracy, remain the method of choice for classification of BSEP inhibitors, structure-assisted docking models demonstrate reasonably good prediction accuracies while additionally providing information about putative protein–ligand interactions.     

A mixed bvp for flow in strongly anisotropic media

Initial-boundary value problems for a class of linear parabolic equations are considered. The anisotropy of the medium is characterised by a small parameter. The solution structure is analysed by singular perturbation methods which include the construction of outer solutions and boundary and initial layer terms. The analysis is justified by convergence results