金融复制因子动态：系统性风险规避策略的出现
Financial replicator dynamics: emergence of systemic-risk-averting strategies
摘要：
我们考虑一个随机的金融网络与大量的代理人。代理人通过相互借贷的信贷工具或通过直接借贷进行联系，这些都产生了负债。合同期结束时各代理人的债务清偿问题可以表示为随机不动点方程的解。我们的第一步是获得这些解决方案（渐近），使用最近的结果随机不动点方程。我们考虑了一个大的人口，代理人适应两个可用的策略，风险或无风险的投资，以最大化他们的预期收益率（或盈余）。我们的目标是研究新出现的策略时，不同类型的复制动力学捕获代理间的相互作用。我们从理论上减少了复杂系统的分析，一个适当的常微分方程（ODE）。我们证明了平衡策略几乎必然收敛于常微分方程的吸引子。我们还推导出一个混合进化稳定策略（ESS）出现的条件下，在这些情况下，复制动态收敛到一个均衡，在这个均衡中，两个种群的预期收益率是相等的。此外，平均动态（基于大的观察样本的选择）总是避免系统性风险事件（违约率高的事件）。我们通过蒙特卡罗模拟验证了由常微分方程方法建议的平衡确实代表了动力学的极限。
英文摘要：
We consider a random financial network with a large number of agents. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liabilities. The settlement of the debts of various agents at the end of the contract period can be expressed as solutions of random fixed point equations. Our first step is to derive these solutions (asymptotically), using a recent result on random fixed point equations. We consider a large population in which agents adapt one of the two available strategies, risky or risk-free investments, with an aim to maximize their expected returns (or surplus). We aim to study the emerging strategies when different types of replicator dynamics capture inter-agent interactions. We theoretically reduced the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). We proved that the equilibrium strategies converge almost surely to that of an attractor of the ODE. We also derived the conditions under which a mixed evolutionary stable strategy (ESS) emerges; in these scenarios the replicator dynamics converges to an equilibrium at which the expected returns of both the populations are equal. Further the average dynamics (choices based on large observation sample) always averts systemic risk events (events with large fraction of defaults). We verified through Monte Carlo simulations that the equilibrium suggested by the ODE method indeed represents the limit of the dynamics.
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