A multi-agent equilibrium model in an incomplete market with discrete dividends: Applications to long-term discount curves

This paper develops a multi-agent equilibrium model in an incomplete market setting. The model incorporates dividend-paying securities whose dividend processes are interpreted as flows of consumption goods and can be driven by exogenously given factor processes. We consider an optimal consumption and portfolio problem for agents who have different views on fundamental risks and heterogeneous time preferences. Using a convex duality approach, we obtain expressions for the equilibrium state price density process, which subsequently yields the term structure of discount rates. To better reflect market practices, the model also incorporates discrete timing for dividend payments, consistent with semiannual or annual coupon schedules and policy decisions that typically occur at specific points during the year. As an application of the model, we provide numerical examples of long-term discount rates for valuing long-dated cashflows while exogenously incorporating the dynamics of factor processes that drive the dividend processes reflecting changes in the amount of government bonds available in the market. We examine how changes in the supply of government bonds affect the pricing of insurance products, including death benefits and pension annuities, through shifts in long-term discount rates. The numerical examples illustrate the qualitative implications of the model and are not intended to provide empirical findings.