Super-Long Discount Rates for Insurers in Incomplete Markets with Bond Supply Control

This paper develops a multi-agent equilibrium model in an incomplete market setting and derives super-long discount rates for insurance companies, while exogenously incorporating the dynamics of government financing and central bank operations in purchasing government bonds. Specifically, we include dividend-paying securities in the model that represent the market value of outstanding government bonds, categorized by their time to maturity, and consider an optimal consumption and portfolio problem of agents who have different views on fundamental risks and heterogeneous time preferences. Using a convex dual problem approach, we obtain expressions for the equilibrium state price density process. Moreover, we derive the yield curve for discount rates in equilibrium, associating exogenously determined dividend processes with coupon payments from the government bonds categorized by time-to-maturity, which reflect market outstanding notional adjustments. The main contribution of our study is the incorporation of changes in the supply of government bonds in the secondary market into the incomplete market equilibrium model. This approach enables us to estimate the impact of net supply changes of the government bonds on super-long discount rates, while incorporating the heterogeneous views of agents regarding fundamental risks, represented by Brownian motion. Finally, we examine how changes in the supply of government bonds impact the pricing of insurance products, including death benefits and pension annuities, through shifts in the super-long discount rates.