# Tag Info

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Recursive Utility The traditional approach to consumption-based asset pricing includes time separable (additive) expected utility functions, $$U(C_t,C_{t+1})=u(C_t)+\beta \mathbb{E}_t[u(C_{t+1})],$$ where $\beta<1$ measures impatience (subjective discount factor). That's the first equation in Chapter 1.1. in Cochrane's stellar asset pricing book. This ...

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The risky and riskless assets follow processes, $$\frac{dS_t}{S_t}= \mu \, dt + \sigma \, dB_t, \,\,\, \frac{dM_t}{M_t}= r \, dt$$ If the proportion invested in the risky asset at time $t$ is $p_t$, then the wealth process is $$\frac{dX_t}{X_t}= p_t \frac{dS_t}{S_t}+ (1-p_t)\frac{dM_t}{M_t}= (r + p_t(\mu -r)) dt + p_t \sigma dB_t$$ Finding the process for a ...

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There are a few papers out there. A good starting point os the (always relevant) Grossman and Stiglitz (1980) "On the Impossibility of Informationally Efficient Markets" which shows that markets cannot be perfectly efficient without analysts being rewarded for their efforts (and is mentioned by many of the following articles as explaining some of ...

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I want to add two comments to this. 1. Empirical utility-based-optimization and moments I would argue that comparing different degrees of a Taylor approximated utility optimization (a.k.a. a moment based model with two, three, four, ..., infinite moments) adds additional assumptions to your model when working with an asset universe whose statistics are not ...

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If utility is your measure of performance, then it will still be your measure of performance out of sample, since it is what you care about. You can see utility as a measure of the balance between profit and risk, where risk is some combination of variance, skew, kurtosis... Your wealth is a random variable $X$ that can be described by its moments. First ...

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yes that is of course possible. If you set up the corresponding optimisation, $$L=w^T\mu - \frac{\lambda}{2}w^T\Sigma w - h\left(w^T\mathbf{1}-1\right)$$ and find the first order conditions: $$\begin{pmatrix} \lambda\Sigma & \mathbf{1}\\ \mathbf{1}^T&0 \end{pmatrix}\begin{pmatrix}w\\h\end{pmatrix}=\begin{pmatrix}\mu \\ 1\end{pmatrix}$$ you ...

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EDITED FROM INITIAL POST I am sorry that I took so long to edit this. I have been swamped. Let me first motivate quadratic utility before we tear it apart and talk about the implications of tearing it apart. EDIT TO INCLUDE ANSWER TO 1 I believe implicit in your posting that you are scratching your head because it would seem that quadratic utility has ...

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