A Study on Differential Games with Applications to Asset Management and Market-Liquidity Research.

摘要

The strategic interaction between multiple players under possible sources of uncertainty is an important modeling tool to explain many phenomena in economics and particularly finance. This dissertation makes contribution to the theoretic foundation of differential game models, and highlights its finance applications ranging from asset management to market-liquidity research.;Related to the fundamental theory of differential games, we call attention to the issue of "Consistency of Equilibria Under Equivalent State-Space Representations", and show an analytically explicit example that Nash equilibrium under open-loop structure, even with deterministic system dynamics, can be inconsistent under equivalent state-space representations. On the other hand, we provide a proof that a Nash equilibrium under closed-loop structure is always consistent given any diffeomorphic transform of the state-space. The second contribution of this dissertation is dedicated to an asset management application, and develops an analytically tractable model to address the strategic endowment spending problem with N idiosyncratic players. Henceforth we reveal through comparative static analysis, how the change in one player's time-preference and/or risk-preference affects the equilibrium spending policy of himself and his peer players. Besides, we are able to draw conclusions on the asymptotic trend of the endowment's evolution under equilibrium, and discuss how the asymptotic trend switches regime as various parameters of the game vary in value. The third contribution of this dissertation, dedicated to market-liquidity research, develops a game-theoretic model allowing closed-loop strategies for strategic players in the so-called "predatory trading", where the noise traders aggregate also play a non-trivial role in the evolution of this happening. This improves from the previous open-loop models where it is solely a deterministic game between the oligopolistic players but the rest market participants do not matter at all -- a major confinement of the preceding studies on this topic. Through such, we are able to reveal how market volatility matters as a third important predictor for predatory trading, besides market plasticity and market elasticity.