Continuous-time evolutionary stock and bond markets with time-dependent strategies

Abstract

This paper develops a general continuous-time evolutionary finance model with time-dependent strategies based on evolutionary game theory. We show 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. We study in detail, a deterministic evolutionary bond market and certify that a bond market is evolutionary stable if and only if the total returns across all assets are the same. By this way, we derive an explicit expression for the bond valuation and provide an approach to recover the benchmark interest rate from an effective bond market. Key words: Evolutionary finance, evolutionary bond market, continuous-time model, time-dependent strategies.