The dynamics of risk-sensitive allocations

This paper describes Pareto optimal allocations when agents have risk-sensitive preferences as formulated by Hansen and Sargent (1995). Necessary and sufficient conditions are given for the existence of a steady state at which Pareto weights are time-invariant. Sufficient conditions are given for steady states to be stable or unstable. When all agents are risk-sensitive with power reward functions there is a unique interior steady state. This steady state is stable when the power is positive and unstable when the power is negative. When there is at least one agent with time-additive preferences eventually all risk-sensitive agents have zero Pareto weights.