Risk Theory with Affine Dividend Payment Strategies

We consider a classical compound Poisson risk model with affine dividend payments. We illustrate how both by analytical and probabilistic techniques closed-form expressions for the expected discounted dividends until ruin and the Laplace transform of the time to ruin can be derived for exponentially distributed claim amounts. Moreover, numerical examples are given which compare the performance of the proposed strategy to classical barrier strategies and illustrate that such affine strategies can be a noteworthy compromise between profitability and safety in collective risk theory

Tur\'an Graphs, Stability Number, and Fibonacci Index

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.Comment: 11 pages, 3 figure

Contributions to digit expansions with respect to linear recurrences

AbstractExtensions and improvements of a recent paper, “On Digit Expansions with Respect to Linear Recurrences” by A. Pethö and R. F. Tichy (J. Number Theory 33 (1989), 243–256) are established. Furthermore distribution properties mod 1 of the sequence (xsG(n)) are investigated, where sG(n) denotes the sum-of-digits function with respect to the linear recurrence G

Associativity of recurrence multiplication

An extension of Knuth's Fibonacci multiplication to recurrences Gk+d = a1Gk+d-1 + + adGk with a1 = a2 = = ad 2>0 and "canonical" initial values Gk = a1Gk-1 + a2Gk-2 + + akG0 + 1, 0 = k <d is established. We prove associativity for this multiplication if a related parameter is chosen sufficiently large