Actuarial Science and Financial Mathematics seminar series
Yiying Zhang
Southern University of Science and Technology
Room: M3 3127
Insurance demand under government interventions and distorted probabilities
In the catastrophe insurance market, government interventions are common. This talk studies optimal insurance demand for an individual under distorted probabilities with the participation of government interventions, such as premium subsidies and disaster relief. We model the premium subsidy as a non-decreasing function ranging between 0 and 1, representing the percentage of the government support, whereas the relief assistance is characterized by a 1-Lipschitz relief scheme function, reflecting the effort of the government in post-disaster recovery. When the expected value premium principle is employed, the general form of the optimal retained loss function for the insured is derived by jointly applying the calculus of variations and the marginal indemnification function approach when the relief scheme function is concave. We demonstrate that the optimal retained loss function takes a layered form, shaped by the trade-off between government premium subsidies and relief assistance, and can be further characterized by an ordinary integro-differential equation. In particular, explicit solutions are obtained for VaR, TVaR, and general convex distortion risk measures. To provide further insights, we explore two nontrivial extensions. Numerical examples are also provided to illustrate and validate the main findings.