{"ID":2890183,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.19959","arxiv_id":"2507.19959","title":"Self-protection and self-insurance for general risk models via a BSDE approach","abstract":"We investigate an optimal prevention and insurance problem in a general risk setting, where a representative agent is exposed to potential losses. The agent adopts a strategy that combines self-protection, aimed at reducing the frequency of claims, and self-insurance, aimed at mitigating their severity. The problem, which consists in maximizing the expected exponential utility of terminal wealth, is formulated as a stochastic control problem and solved by means of backward stochastic differential equations (BSDEs). Our approach, essentially based on a general Bellman Optimality Principle (see [13] among others), does not require specification of the underlying filtration structure, making it applicable to a broad class of risk models, including Markov-modulated, stochastic factor, Cox-shot noise and self-excited models. We extend recent results by [3, 5], which focused on self-protection in specific models, by allowing for both self-protection and self-insurance within a unified and general framework.","short_abstract":"We investigate an optimal prevention and insurance problem in a general risk setting, where a representative agent is exposed to potential losses. The agent adopts a strategy that combines self-protection, aimed at reducing the frequency of claims, and self-insurance, aimed at mitigating their severity. The problem, wh...","url_abs":"https://arxiv.org/abs/2507.19959","url_pdf":"https://arxiv.org/pdf/2507.19959v1","authors":"[\"Claudia Ceci\",\"Alessandra Cretarola\"]","published":"2025-07-26T14:17:20Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Large Language Model\"]","has_code":false}