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This article focuses on analyzing the finite-time ruin probability within a specific class of discrete risk models. These models incorporate dependent claims, an interest rate component, and stationary noise terms exhibiting semi-heavy-tailed behavior. In this framework, the claim amount follows a unilateral linear dependent process with independent and identically distributed noise terms, while the discount factor is determined by both the interest rate and time. The finite-time ruin probability has been derived under insurance risk conditions resembling the gamma distribution.

Interkingdom signalling within a holobiont allows host and symbionts to communicate and to regulate each other’s physiological and developmental states. Here we show that a suite of signalling molecules that function as neurotransmitters and neuromodulators in most animals with nervous systems, specifically dopamine and trace amines, are produced exclusively by the bacterial symbionts of the demosponge Amphimedon queenslandica. Although sponges do not possess a nervous system, A. queenslandica expresses rhodopsin class G-protein-coupled receptors that are structurally similar to dopamine and trace amine receptors. When sponge larvae, which express these receptors, are exposed to agonists and antagonists of bilaterian dopamine and trace amine receptors, we observe marked changes in larval phototactic swimming behaviour, consistent with the sponge being competent to recognise and respond to symbiont-derived trace amine signals. These results indicate that monoamines synthesised by bacterial symbionts may be able to influence the physiology of the host sponge.