# Tag Info

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### Anyone has detailed explanation on how to use epstein-zin preferences in asset pricing models

Recursive Utility The traditional approach to consumption-based asset pricing includes time separable (additive) expected utility functions, $$U(C_t,C_{t+1})=u(C_t)+\beta \mathbb{E}_t[u(C_{t+1})],$$ ...
• 15.9k

### Application of Ito's Lemma in expected utility theory

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 $p_t$, ...
• 3,650
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### Why are some utility functions widely used?

These are a natural and easiest (most tractable mathematically) choice. A utility function is defined up to a positive affine transformation: economically there is no difference between the utility ...
• 5,080

### Utility Theory and Mean Variance Analysis

Theoretically: no. For most practical purposes: yes; given that risks are small risks, see these lecture notes on p76. Belows's the background and one example showing you why you can run into ...
• 6,554
Accepted

### example Hamilton-Jacobi-Bellman Equation - clarification of $dX_t$ derivation using $\pi_t$, $\Pi_t$

We assume that \begin{align*} \frac{dX_t}{X_t} &= (r+\pi Y_t)dt + \pi\sigma dW_t,\tag{1}\\ dY_t &= -\lambda Y_t + dB_t.\tag{2} \end{align*} From $(2)$, \begin{align*} Y_t = Y_0 e^{-\lambda t}...
• 21.1k

### Why do we assume quadratic utility in portfolio theory?

The assumption of quadratic utility function is convenient in portfolio theory because it is possible to demonstrate that if the portfolio returns are not normally distributed, the mean-variance ...
• 324
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• 2,422

### Are Insurance and Risk premium totally different?

An Insurance premium typically focuses solely on the downside of your Risk. An Insurance pays if you suffered some damage, but you do not give them some share of your profit if things are good. That ...
• 828
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### Utility function for avoiding investment

Assuming that $W_0$ is the initial wealth and that $\alpha$ and $\beta$ are yields of return, the final wealth is a discrete random variable \begin{align} W_T = \begin{cases} W_0(1+\alpha) &\text{ ...
• 14.6k
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• 6,554
1 vote

### Fixes of quadratic utility when probability of decreasing utility is large

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 ...
• 4,299
1 vote

### Risk neutrality coherence with risk aversion

If you make the assumption that the market is complete and that there is no arbitrage then the risk neutral measure exists which allows to price each asset as an expectation of the asset’s future ...
• 2,187
1 vote
Accepted

### Does CRRA-utility imply higher risk-aversion for lower wealth?

It depends on what you mean by risk aversion. The utility function you mention is called "CRRA - Constant Relative Risk Aversion Utility". As the name implies it has constant relative risk aversion (...
• 8,306
1 vote

### Debreu's Representation Theorem proof

A function $f: X \to Y$ is continuous if for every open set $V$ in $Y$, the preimage $f^{-1}(V)$ is open in $X$. Any open subset of the reals, which is not the empty set, is an open interval or the ...
• 111
1 vote
Accepted

### Why is this utility function not picking up its penalty?

The problem was a missing $W_t$ in the equation for correlation. I've updated the above code and did a rerun. We have now the following allocation which is much closer to the Infanger paper. ...
• 1,718

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