Interplay of insurance and financial risks in a discrete-time model with strongly regular variation

Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting from investments. Its wealth process is described in a standard discrete-time model in which, during each period, the insurance risk is quantified as a real-valued random variable $X$ equal to the total amount of claims less premiums, and the financial risk as a positive random variable $Y$ equal to the reciprocal of the stochastic accumulation factor. This risk model builds an efficient platform for investigating the interplay of the two kinds of risk. We focus on the ruin probability and the tail probability of the aggregate risk amount. Assuming that every convex combination of the distributions of $X$ and $Y$ is of strongly regular variation, we derive some precise asymptotic formulas for these probabilities with both finite and infinite time horizons, all in the form of linear combinations of the tail probabilities of $X$ and $Y$. Our treatment is unified in the sense that no dominating relationship between $X$ and $Y$ is required.Comment: Published at http://dx.doi.org/10.3150/14-BEJ625 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Scalability of Hydrodynamic Simulations

Many hydrodynamic processes can be studied in a way that is scalable over a vastly relevant physical parameter space. We systematically examine this scalability, which has so far only briefly discussed in astrophysical literature. We show how the scalability is limited by various constraints imposed by physical processes and initial conditions. Using supernova remnants in different environments and evolutionary phases as application examples, we demonstrate the use of the scaling as a powerful tool to explore the interdependence among relevant parameters, based on a minimum set of simulations. In particular, we devise a scaling scheme that can be used to adaptively generate numerous seed remnants and plant them into 3D hydrodynamic simulations of the supernova-dominated interstellar medium.Comment: 12 pages, 1 figure, submitted to MNRAS; comments are welcom