A spatial modelling framework for assessing climate change impacts on freshwater ecosystems: Response of brown trout (Salmo trutta L.) biomass to warming water temperature

Mountain regions worldwide are particularly sensitive to on-going climate change. Specifically in the Alps in Switzerland, the temperature has increased twice as fast than in the rest of the Northern hemisphere. Water temperature closely follows the annual air temperature cycle, severely impacting streams and freshwater ecosystems. In the last 20 years, brown trout (Salmo trutta L) catch has declined by approximately 40-50% in many rivers in Switzerland. Increasing water temperature has been suggested as one of the most likely cause of this decline. Temperature has a direct effect on trout population dynamics through developmental and disease control but can also indirectly impact dynamics via food-web interactions such as resource availability. We developed a spatially explicit modelling framework that allows spatial and temporal projections of trout biomass using the Aare river catchment as a model system, in order to assess the spatial and seasonal patterns of trout biomass variation. Given that biomass has a seasonal variation depending on trout life history stage, we developed seasonal biomass variation models for three periods of the year (Autumn-Winter, Spring and Summer). Because stream water temperature is a critical parameter for brown trout development, we first calibrated a model to predict water temperature as a function of air temperature to be able to further apply climate change scenarios. We then built a model of trout biomass variation by linking water temperature to trout biomass measurements collected by electro-fishing in 21 stations from 2009 to 2011. The different modelling components of our framework had overall a good predictive ability and we could show a seasonal effect of water temperature affecting trout biomass variation. Our statistical framework uses a minimum set of input variables that make it easily transferable to other study areas or fish species but could be improved by including effects of the biotic environment and the evolution of demographical parameters over time. However, our framework still remains informative to spatially highlight where potential changes of water temperature could affect trout biomass. (C) 2015 Elsevier B.V. All rights reserved.-

Randomized observation periods for the compound Poisson risk model: Dividends

In the framework of the classical compound Poisson process in collective risk theory, we study a modification of the horizontal dividend barrier strategy by introducing random observation times at which dividends can be paid and ruin can be observed. This model contains both the continuous-time and the discrete-time risk model as a limit and represents a certain type of bridge between them which still enables the explicit calculation of moments of total discounted dividend payments until ruin. Numerical illustrations for several sets of parameters are given and the effect of random observation times on the performance of the dividend strategy is studied.

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).

A risk model with an observer in a Markov environment

We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.