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

In: Heterogeneous Agents in Asset Pricing, Vol 1

Author

Listed:
  • Hamilton Galindo Gil

    (Cleveland State University, Department of Finance and Economics
    Universidad ESAN, Graduate School of Business)

Abstract

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)).

Suggested Citation

  • Hamilton Galindo Gil, 2025. "A General Equilibrium Model with Log Utility Function and One State Variable," Lecture Notes in Economics and Mathematical Systems, in: Heterogeneous Agents in Asset Pricing, Vol 1, chapter 0, pages 223-240, Springer.
    • Handle: RePEc:spr:lnechp:978-3-031-93263-2_7
    DOI: 10.1007/978-3-031-93263-2_7
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