{"ID":5346740,"CreatedAt":"2026-06-30T04:09:55.830587294Z","UpdatedAt":"2026-07-02T14:12:34.668891255Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.30363","arxiv_id":"2606.30363","title":"Strategic Risk Reduction: Self-Protection and Self-Insurance","abstract":"This paper studies how a risk holder should combine self-protection and self-insurance when market insurance is absent. In a Bernoulli loss model, self-protection reduces the residual loss probability, while self-insurance reduces the residual loss severity. The risk holder evaluates residual risk using either Value-at-Risk or Tail Value-at-Risk and incurs a joint risk-reduction cost that allows technological interaction between the two activities. We show that Value-at-Risk leads to a threshold-driven solution that the optimal strategy is either no risk reduction, pure self-protection, or pure self-insurance. By contrast, Tail Value-at-Risk creates a direct interaction between residual frequency and residual severity, making the problem non-convex even in the Bernoulli setting. We solve it using an isoquant geometry method based on the marginal-balance curves for self-protection and self-insurance. The analysis identifies when optimal strategies lie on boundaries, extreme constrained candidates, touching components, or crossing components, and shows how the confidence level and the cost technology determine whether self-protection and self-insurance behave as substitutes or complements.","short_abstract":"This paper studies how a risk holder should combine self-protection and self-insurance when market insurance is absent. In a Bernoulli loss model, self-protection reduces the residual loss probability, while self-insurance reduces the residual loss severity. The risk holder evaluates residual risk using either Value-at...","url_abs":"https://arxiv.org/abs/2606.30363","url_pdf":"https://arxiv.org/pdf/2606.30363v1","authors":"[\"Wing Fung Chong\"]","published":"2026-06-29T14:27:40Z","proceeding":"q-fin.RM","tasks":"[\"q-fin.RM\",\"math.OC\"]","methods":"[]","has_code":false}