Adjustment coefficient for risk processes in some dependent contexts

Following an article by Muller and Pflug, we study the adjustment coefficient of ruin theory in a context of temporal dependency. We provide a consistent estimator of this coefficient, and perform some simulations.

💡 Research Summary

This paper extends the classical adjustment coefficient concept from ruin theory to risk processes that exhibit temporal dependence. Starting from the independent‑loss framework, the authors consider a surplus process (R_t = u + ct - \sum_{i=1}^{N(t)} X_i) where the claim sizes (X_i) are not i.i.d. but follow a dependent structure, primarily a Markov chain or a weakly dependent time series. The adjustment coefficient (\theta) is defined as the positive solution of the conditional moment‑generating equation (\mathbb{E}