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This chapter makes other refinements on the model introduced in Chap. 5 by assuming that agent’s preferences are represented by a logarithm utility function, and the investment opportunities are reduced to one risky asset, one production activity, and the riskless asset. Furthermore, we assume that there exists only one exogenous state variable. Under these assumptions, we show that the riskless rate, price of risk, and optimal consumption are easy to determine. However, we need to solve a PDE using numerical methods to obtain the price of the risky asset and hence its volatility. This model has been typically used to study the term structure of the interest rate. This chapter is also based on Cox et al. (Econometrica, 53(2), 385–407 (1985b)).

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A General Equilibrium Model with Log Utility Function and One State Variable

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  • 发表日期：

    2025年

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  • Hamilton Galindo Gil

摘要

This chapter makes other refinements on the model introduced in Chap. 5 by assuming that agent’s preferences are represented by a logarithm utility function, and the investment opportunities are reduced to one risky asset, one production activity, and the riskless asset. Furthermore, we assume that there exists only one exogenous state variable. Under these assumptions, we show that the riskless rate, price of risk, and optimal consumption are easy to determine. However, we need to solve a PDE using numerical methods to obtain the price of the risky asset and hence its volatility. This model has been typically used to study the term structure of the interest rate. This chapter is also based on Cox et al. (Econometrica, 53(2), 385–407 (1985b)).