| Abstract: |
| This talk introduces McKean--Vlasov stochastic differential equations to model insurance reserves in a large, interacting pool of insurers. Our framework departs from the classical Cram\`er--Lundberg model by letting premiums and claim distributions adapt to the evolving cross-sectional distribution of capital, thereby capturing feedback and contagion effects. Using characteristic-function based integral and recursive formulas together with iterative moment calculations, we track distributional dynamics over time and design adaptive premium and systemic risk measures. These methods yield distribution-sensitive adjustment coefficients and supermartingale bounds for ruin probabilities, updating classical ruin theory for modern interconnected insurance markets. |
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