Continuous-Time Evolutionary Stock and Bond Markets with Time-Dependent Strategies

This paper develops a general continuous-time evolutionary finance model with time-dependent strategies. It is shown that the continuous model, which is a limit of a general discrete model, is well-defined and if there exists one completely diversified strategy in the market, then there is no sudden bankruptcy. After that a deterministic evolutionary bond market is studied in detail. It is certified that a bond market is evolutionary stable, which is equal to arbitrage-free if and only if the total returns defined in this paper across all the assets are the same, or each bond is evaluated by an improper integral in which the integrand is a discounted value of the dividend payoff with the discount rate being market consumption parameter. Last an approach to compute the benchmark interest rate is provided.