Stochastic model of illiquid asset trade

This work studies the behavior of a consumer who seeks to allocate his welfare optimally between risk-free saving and a risky illiquid asset. The risk of the illiquid asset emerges from inability to trade it at an arbitrary moment of time. Instead, the illiquid asset may be traded at random discrete moments of time. It is assumed that the trader receives a certain utility from the amount of the illiquid asset he owns. A stochastic optimization model of the trader behavior is proposed and analyzed. This analysis is applied to modeling a market with multiplicity of traders. It is shown that even under conditions of perfect foresight, the equilibrium price dynamics may have a shape characteristic of a ≪financial bubble≫.