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This chapter derives the wealth dynamics in continuous time, a fundamental component of the agent’s optimal control problem. The analysis begins by defining the agent’s budget constraint in discrete time. Subsequently, the budget constraint and the wealth equation are transformed into their continuous-time counterparts. These expressions are then integrated to formulate the agent’s continuous-time wealth dynamics. The chapter concludes with two illustrative examples.

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Wealth Dynamics

  • 章节

  • 发表日期：

    2025年

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  • Hamilton Galindo Gil

摘要

This chapter derives the wealth dynamics in continuous time, a fundamental component of the agent’s optimal control problem. The analysis begins by defining the agent’s budget constraint in discrete time. Subsequently, the budget constraint and the wealth equation are transformed into their continuous-time counterparts. These expressions are then integrated to formulate the agent’s continuous-time wealth dynamics. The chapter concludes with two illustrative examples.