Two-Person Dynamic Equilibrium in the Capital Market

When several investors with different risk aversions trade competitively in a capital market, the allocation of wealth fluctuates randomly among them and acts as a state variable against which each market participant will want to hedge. This hedging motive complicates the investors' portfolio choice and the equilibrium in the capital market. This article features two investors, with the same degree of impatience, one of them being logarithmic and the other having an isoelastic utility function. They face one risky constant-return-to-scale stationary production opportunity and they can borrow and lend to and from each other. The behaviors of the allocation of wealth and of the aggregate capital stock are characterized, along with the behavior of the rate of interest, the security market line, and the portfolio holdings.