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Main Authors: Ceci, Claudia, Cretarola, Alessandra
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.19959
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author Ceci, Claudia
Cretarola, Alessandra
author_facet Ceci, Claudia
Cretarola, Alessandra
contents 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.
format Preprint
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publishDate 2025
record_format arxiv
spellingShingle Self-protection and self-insurance for general risk models via a BSDE approach
Ceci, Claudia
Cretarola, Alessandra
Optimization and Control
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.
title Self-protection and self-insurance for general risk models via a BSDE approach
topic Optimization and Control
url https://arxiv.org/abs/2507.19959