UCSB Financial Math
Student Seminar (FMSS)

Speakers: Juan Diego Mejía Becerra
Date: 2pm - 4pm, 30 October, Friday
Title: (TBA)

Speakers: Byungdoo Kong
Title: Endogenous Reinsurance Pricing in Large Competitive Insurance Markets: Finite-Player and Mean Field Analysis (Slides)
Abstract:
We consider a competitive reinsurance market with one strategic reinsurer and many heterogeneous insurers. The reinsurer acts as a Stackelberg leader by setting a common premium, while the insurers choose retention and investment strategies under relative performance concerns and common insurance and financial risks.

For a fixed premium, we characterize the insurers’ Nash equilibrium through a scalar fixed point for the population’s average exposure to common insurance risk. This reveals a spillover effect from relative performance concerns: greater aggregate exposure strengthens insurers’ incentives to retain risk, so some may retain even when reinsurance remains actuarially favorable. The resulting threshold structure reduces the reinsurer’s pricing problem to a one-dimensional optimization.

We characterize Stackelberg equilibria in both finite-player and mean-field settings. For the finite-player model, we develop an efficient procedure that avoids enumerating all retention configurations. We also establish convergence from finite-player to mean-field equilibria without assuming the mean-field equilibrium premium is unique.

This is joint work with Ruimeng Hu (UCSB).

• Haosheng Zhou (Princeton University)