Asset Pricing and Earnings Fluctuations in a Dynamic Corporate Economy

We give a new predictive mathematical model for macroeconomics, which deals specifically with asset prices and earnings fluctuations, in the presence of a dynamic economy involving mergers, acquisitions, and hostile takeovers. Consider a model economy with a large number of corporations $C_1, C_2, ..., C_n$ of different sizes. We ascribe a degree of randomness to the event that any particular pair of corporations $C_i, C_j$ might undergo a merger, with probability matrix $p_{ij}$. Previous random-graph models set $p_{ij}$ equal to a constant, while in a real-world economy, $p_{ij}$ is a complicated function of a large number of variables. We combine techniques of artificial intelligence and statistical physics to define a general class of mathematical models which, after being trained with past market data, give numerical predictions for certain quantities of interest including asset prices, earnings fluctuations, and merger/acquisition likelihood. These new models might reasonably be called ``cluster-size models.'' They partially capture the complicated dependence of $p_{ij}$ on economic factors, and generate usable predictions.