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This chapter provides a step-by-step explanation of the Cox et al. (Econometrica, 53(2), 363–384 (1985a)) model, a foundational representative agent framework in continuous-time finance. We carefully derive the wealth dynamics, transform the stochastic optimal control problem into a dynamic programming framework, and present each first-order condition. Additionally, we detail the Hamilton-Jacobi-Bellman (HJB) equilibrium equation and the partial differential equation for asset prices. As a cornerstone of the continuous-time asset pricing literature, this model serves as the basis for more advanced frameworks incorporating representative or heterogeneous agents.

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A General Equilibrium Model with k State Variables

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  • 发表日期：

    2025年

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  • Hamilton Galindo Gil

摘要

This chapter provides a step-by-step explanation of the Cox et al. (Econometrica, 53(2), 363–384 (1985a)) model, a foundational representative agent framework in continuous-time finance. We carefully derive the wealth dynamics, transform the stochastic optimal control problem into a dynamic programming framework, and present each first-order condition. Additionally, we detail the Hamilton-Jacobi-Bellman (HJB) equilibrium equation and the partial differential equation for asset prices. As a cornerstone of the continuous-time asset pricing literature, this model serves as the basis for more advanced frameworks incorporating representative or heterogeneous agents.