An Actuarial Modeling of Forest Insurance to the Extreme Risk of Windthrow Damage

Standard actuarial methods often fail to accurately price the risk of catastrophic events due to the characteristic low frequency and high severity of such occurrences. To address these limitations, two actuarial solutions that integrate current knowledge of extreme value theory (EVT) with the theory of non-life insurance are proposed. To address the extreme risk, the Gumbel distribution (solution E1) and the chi-squared distribution (solution E2) were applied. The applicability of the proposed insurance models against the risk of windthrow damage was demonstrated on Norway spruce (Picea abies L. Karst.) stands at a national scale within the Slovak Republic. The results reveal a crucial economic relationship between the insurance layers: the higher the reliability and cost of coverage in the primary model, the cheaper the subsequent secondary premium for risk of extreme damage becomes. For both assumed return periods of 20-year and 100-year extreme events, the solution E2 generates lower and more acceptable total insurance premiums. Subsequently, both models address effectively the foundational insurance concept of risk minimization through spatial diversification.