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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.19959 |
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| _version_ | 1866909706882121728 |
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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 |
| id |
arxiv_https___arxiv_org_abs_2507_19959 |
| institution | arXiv |
| 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 |