Equilibrium Investment with Random Risk Aversion: (Non-)uniqueness, Optimality, and Comparative Statics

Battle Count: 96

The paper provides important theoretical foundations for portfolio selection under preference uncertainty, which is relevant for quantitative trading strategies that must account for time-varying risk aversion. The closed-form equilibrium strategies and comparative statics results offer insights into how risk exposure should be adjusted. However, the paper is purely theoretical with no backtesting, empirical validation, or implementation guidance. The Black-Scholes assumption and deterministic strategy restriction limit direct applicability to real trading systems. The findings about non-uniqueness of equilibria and the insufficiency of first-order stochastic dominance for comparative statics are conceptually important for strategy design.

The theoretical framework requires advanced knowledge of continuous-time stochastic control, SDEs, ODE theory, measure-theoretic probability, and stochastic orders. The closed-form solutions for specific distributions (Poisson, Gamma) are implementable, but the general framework requires solving ODEs numerically. The comparative statics analysis involves complex mathematical arguments. No code is provided. Implementing the equilibrium strategies requires computing the function h(x) and its integral H(y) for the given RRA distribution, then solving the ODE or applying the closed-form inverse.

The paper is entirely theoretical with complete proofs provided in the main text and appendices. All results are derived analytically from first principles. The closed-form solutions for Poisson and Gamma distributed RRA are explicitly given. However, no code or numerical implementation is provided. Verification requires advanced knowledge of stochastic calculus, ODE theory, and measure-theoretic probability.