Time-consistent investment and reinsurance under relative performance concerns

This article investigates the optimal time-consistent investment and reinsurance for two mean–variance insurance managers who take into account the relative performance by comparison to their peers. The unique time-consistent Nash equilibrium policies and the corresponding value functions are derived for asset concentration and diversification. No matter which case is chosen, when the two insurance managers are sensitive to each other’s wealth, they chase each other’s trading behaviors leading to under-reinsurance and overinvestment and lower utility relative to the standard case without relative concerns. The cost–benefit from asset diversification to asset concentration and economic implications of parameters are illustrated by numerical examples.