Combined Accumulation- and Decumulation-Plans with Risk-Controlled Capital Protection

We base our analysis on an investor, usually a retiree, endowed with a certain amount of wealth W, who considers both his own consumption needs (fixed periodic withdrawals) and the requirement of his heirs (defined bequest). For this purpose he pursues the following in-vestment strategy. The part F is invested in a set of investment funds with the target to achieve an accumulated wealth at the end of a certain time horizon of at least the original amount of wealth W (or the fraction ), measured in real terms. As certain investment risks are implied, we allow for the probability of falling short of the target and implement it into our model as a risk control parameter. The remaining part MM of the original wealth is invested in money market funds in order to avoid additional investment risks and deliver fixed periodic withdrawals until the end of the respective time horizon. The optimal investment strategy is the investment fund allocation that satisfies the probability of shortfall and mini-mizes F, while maximizing the fixed periodic withdrawals. We outline this investment prob-lem in a mathematical model and illustrate the solution for a reasonable choice of empirical parameters.

Time parameters and Lorentz transformations of relativistic stochastic processes

Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell distribution, the associated proper-time parameterized process converges to a modified momentum distribution, differing by a factor proportional to the inverse energy.Comment: 5 pages, 1 figur

Asset/Liability Management of German Life Insurance Companies: A Value-at-Risk Approach in the Presence of Interest Rate Guarantees

This contribution analyses the implications of two major determinants influencing the asset allocation decision of German life insurers, which are the capital market development on the one hand and the interest rate guarantees of the traditional life insurance policies on the other hand. The adverse development of the stock prices between 2000 and 2002 asks for a consideration of not only the �normal� volatility but also the worst-case developments in an asset/liability management. In order to meet the latter requirement, we technically apply the risk measures of Value-at-Risk and Conditional Value-at-Risk. German life insurance policies incorporate interest rate guarantees, which are granted on an annual basis. This specific �myopic� nature of guarantees creates � beyond the control of the shortfall risk in general � the necessity to manage the asset allocation on an annual basis to match the time horizon of assets and liabilities. A quantitative approach analyses the impacts on the asset allocation decision. In our research we do not only consider market valuation, but also institutional peculiarities (such as hidden reserves and accounting norms) of German life insurers. We reveal the possibility of a riskless one-year investment, either based on market values or on book values, to be crucial for guaranteeing interest rates on an annual basis.

Diplodia seriata, cause of black fruit rot in organically grown apples in Holland, Belgium and Northern Germany

A fruit rot resembling Gloeosporium infections but appearing on fruits prior to harvest was noticed in organic apple orchards in Holland, Belgium and Northern Germany in 2007. Infections were most commonly observed on ‘Elstar’, but other cultivars were also affected. Fruit colonisation progressed in two steps, whereby a latent stage of sunken black lesions in immature fruits gave rise to a rapidly spreading firm brown rot upon fruit ripening. Isolation experiments from both stages consistently yielded a single species of fungus identified as Diplodia seriata, formerly known under the teleomorph name Botryosphaeria obtusa. Lesions of D. seriata were also seen on leaves as necrotic light brown spots surrounded by a purple halo, and occasionally on small twigs as cankers. Fruit mummies on apple twigs were heavily colonised by D. seriata and are thus likely to carry inoculum for fruit infections during late summer or in the following growing season