{'fraction_non_alphanumeric': 0.02665441176470588, 'fraction_numerical': 0.014705882352941176, 'mean_word_length': 5.405882352941177, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Recursive Calculation of the Dividend Moments in a Multi-threshold Risk Model

Abstract In this article, we consider the class of risk models with Markovian claim arrivals studied by Badescu et al. (2005) and Ramaswami (2006), among others. Under a multi-threshold dividend structure, we develop a recursive algorithm for the calculation of the moments of the discounted dividend payments before ruin. Capitalizing on the connection between an insurer’s surplus process and its corresponding fluid flow process, our approach generalizes results obtained by Albrecher and Hartinger (2007) and Zhou (2006) in the framework of the classical compound Poisson risk model (with phase-type claim sizes). Contrary to the traditional analysis of the discounted dividend payments in risk theory, we develop a sample-path-analysis procedure that allows the determination of these moments with or without ruin occurrence (separately). Numerical examples are then considered to illustrate our main results and show the contribution of each component to the moments of the discounted dividend payments.