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Copy file name to clipboardExpand all lines: lectures/affine_risk_prices.md
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Empirical difficulties with this specification (the equity premium puzzle, the
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risk-free rate puzzle, and the Hansen-Jagannathan bounds discussed in
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{doc}`advanced:doubts_or_variability`) motivate the alternative approach
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[Doubts or Variability](https://python-advanced.quantecon.org/doubts_or_variability.html)) motivate the alternative approach
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described in this lecture.
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Put bluntly, the model to be studied in this lecture declares the Lucas asset pricing model's stochastic discount factor to be a failure.
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({cite:t}`AngPiazzesi2003`).
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3.*Risk-neutral probabilities*: a change-of-measure representation of the pricing equation.
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4.*Distorted beliefs*: reinterpreting risk price estimates when agents hold systematically
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biased forecasts ({cite:t}`piazzesi2015trend`); see also {doc}`advanced:risk_aversion_or_mistaken_beliefs`.
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biased forecasts ({cite:t}`piazzesi2015trend`); see also [Risk Aversion or Mistaken Beliefs](https://python-advanced.quantecon.org/risk_aversion_or_mistaken_beliefs.html).
Copy file name to clipboardExpand all lines: lectures/survival_recursive_preferences.md
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where $\nu$ is the endogenous discount rate.
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```{note}
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In discrete time, Epstein-Zin preferences aggregate current consumption with a certainty equivalent of future utility via a CES aggregator (see {doc}`advanced:doubts_or_variability`).
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In discrete time, Epstein-Zin preferences aggregate current consumption with a certainty equivalent of future utility via a CES aggregator (see [Doubts or Variability](https://python-advanced.quantecon.org/doubts_or_variability.html)).
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In continuous time there is no "next-period $V_{t+1}$," so {cite:t}`Duffie_Epstein1992a` recast the recursion as a felicity function $F(C,\nu)$ that depends on the agent's own continuation-value rate $\nu$.
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