MARKET FORCES AND DYNAMIC ASSET PRICING

• Published in: Stochastic analysis and applications Vol. 20; no. 5; pp. 1027 - 1082
• Main Authors: Peskir, G., Shorish, J.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 11.01.2002; Taylor & Francis
• Subjects: (Geometric) Brownian motion; Accelerated frame of reference; Applied sciences; Asset pricing; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Inertial frame of reference; JEL Subject Classification: C60; G12; G13; Lévy process; Market force; Market microstructure; Markov property; Mathematics; Mathematics Subject Classification 2000: Primary 91B24; 91B28; 91B50; 93E20; Secondary 91A15; 60G51; 60J60; 60J65; Newtonian mechanics; Operational research and scientific management; Operational research. Management science; Optimal control; Optimal stochastic control; Ornstein-Uhlenbeck process; Portfolio theory; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Smoluchowski's approximation; Stochastic processes; The Hamilton-Jacobi-Bellman equation; Markov process; Market structure; Bellman equation; Probabilistic approach; Lévy process; Stochastic game; Brownian motion; Stochastic control(mathematics); Stochastic analysis; Hamilton Jacobi equation; Classical mechanics; Smoluchowski approximation; Newton theory; Ornstein Uhlenbeck process; Market equilibrium; Dynamic model; Market force; Optimal control (mathematics); Asset pricing
• ISSN: 0736-2994; 1532-9356
• DOI: 10.1081/SAP-120014553

We study a dynamic model of asset pricing which is driven by two characteristic market features: the law of investor demand (e.g., "buy low, sell high") and the law of the market institution (which codifies the trading rules under which the market operates). We demonstrate in a simple investor-specialist trading market that these features are sufficient to guarantee an equilibrium where investors' trading strategies and the specialist's rule of price adjustments are best responses to each other. The drift term appearing in the resulting equation of the asset price process may be interpreted using Newtonian mechanics as the acceleration of a "market force." If either of the market participants is risk-neutral, the result leads to risk-neutral asset pricing (e.g., the Black and Scholes option pricing formula).