Finance is the application of mathematical and economical principles to decision-making, in which the allocation of money is performed under conditions of uncertainty (Drake and Fabozzi, 2010). Typically the goal of a financial decision is to maximize profit, all the while maintaing an optimal level of uncertainty in the forward-looking performance of a financial instrument. How market participants perceive the strength of a financial instrument, however, can drastically influence its value, which in turn affects preceding financial decisions. Herd mentality, the notion that people are influenced by their peers to believe, uncritically, that something must be true, can therefore amplify and contort the true market sentiment towards a given instrument, resulting in highly volatile markets and irrational financial decision-making.
In this paper we simplify the dynamics of financial markets by considering a dynamical system comprised of people in a movie theater. Members of the population are free to leave or re-enter the theater based on their perception of the “theater sentiment”. Our objective is to quantify the critical threshold value, CT , that distinguishes between a system in which members act rationally, and one which is dominated by herd mentality (Welling, 2010). To validate our results we present an analogous stochastic model of this system, whose mean outcome, upon multiple simulations, approximates that of the deterministic system of differential equations. Lastly we modify our original model to include a population of two classes, with varying sensitivity levels, σ, to the theater sentiment. We show that concrete quantification of such systems becomes increasingly more difficult as the number of variables, and variable interactions increases. We conclude by considering the population composition of realistic financial systems to demonstrate why all financial markets are ultimately left to the mercy of herd mentality.
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