10 votes
Accepted

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, $$U(C_t,C_{t+1})=u(C_t)+\beta \mathbb{E}_t[u(C_{t+1})],$$ ...
Kevin's user avatar
  • 15.7k
6 votes

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 $p_t$, ...
RRL's user avatar
  • 3,620
6 votes
Accepted

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 ...
olaker's user avatar
  • 5,060
4 votes
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}...
Gordon's user avatar
  • 21.1k
4 votes

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 ...
markowitz's user avatar
  • 324
4 votes
Accepted

Prove that the portfolio that maximizes utility lies on the efficient frontier

The efficient frontier is defined as the set of portfolios which have the highest return for a given measure of volatility, i.e. $\{S: s \in P \; s.t. \nexists \; t \in P \; \text{where} \;R(s) < R(...
Attack68's user avatar
  • 9,939
4 votes
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What is the relation between Relative Risk Aversion and Market Price of Risk

In most economic models the risk aversion coefficient is definitely related to the equity premium. Assuming utility is CRRA (as you mention): \begin{equation} U(C_t) = \frac{C_t^{1-\gamma}}{1-\...
phdstudent's user avatar
  • 8,041
4 votes

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 ...
Kermittfrog's user avatar
  • 6,535
3 votes

Finding parameters of an utility function in a market making strategy to apply it in practice

All the parameters of the solution need to be estimated for your specific stock. Stochastic process-specific parameters, i.e. $\mu$, $\sigma$, have to be estimated by some classical method (e.g. MLE, ...
ragoragino's user avatar
3 votes

Is positive skewness preferences rational or irrational?

I think the usual argument is that if an investor is maximizing expected log wealth, then this implies preference for higher odd order moments (mean return, skew, etc.) and for lower even order ...
steveo'america's user avatar
3 votes
Accepted

ETF pricing papers

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 ...
kurtosis's user avatar
  • 2,880
3 votes

How to compare mean-variance-skewness-kurtosis portfolios obtained by expected utility maximization?

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 ...
Kermittfrog's user avatar
  • 6,535
3 votes

How to compute the mean for utility function?

Maybe you misinterpreted the protection? Also, utility does not stand in $\\\$$. I'd come up with $$ \frac{1}{100}\int_0^{100}(150-43-0.2t)^{2/3}\mathrm{d}t=21.103 $$
Kermittfrog's user avatar
  • 6,535
3 votes

How do your solve for trader's optimal demand in market similar to Kyle's model?

Generic knowledge about this kind of models Let me try to get your model close to elements that are known: Time continuous Kyle's model is something that is solved in Çetin, Umut, and Albina Danilova....
lehalle's user avatar
  • 11.9k
2 votes

Why do we assume quadratic utility in portfolio theory?

The capital asset pricing model (CAPM) is based on mean-variance utility; investors choose their portfolio based only on its mean and variance. This is an entirely different approach than expected ...
Fab's user avatar
  • 345
2 votes

Why do we assume quadratic utility in portfolio theory?

In most settings, utility functions are defined up to an affine transformation: if $u(x)$ defines the preference of an investor, then so does $a*u(x)+b.$ This implies, you can normalize the Taylor ...
LazyCat's user avatar
  • 1,551
2 votes

Why are some utility functions widely used?

The functions are set up so that maximizing the expectation of the utility function will obey the von Neumann-Morgenstern axioms (completeness, transitivity, independence, continuity). As you've ...
elleciel's user avatar
  • 239
2 votes

Utility-optimal leverage with costs

I hope my computations are correct. Let $u(t,x)=\max_{(f_s)_{s\geq t}}\mathbb{E}[(b+X^{f_.}_T)^\gamma]$. Using HJB (you have to prove that it is ok to use it). $$0=\max_{f}\partial_t u(t,x)+(\mu f ...
M. Jeunesse's user avatar
  • 2,422
2 votes

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 ...
Ami44's user avatar
  • 828
2 votes
Accepted

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{ ...
Quantuple's user avatar
  • 14.6k
2 votes
Accepted

Differentiating risk aversion based on utility theory

$$-x \frac{d^2U}{dx^2}=(ax+b)\frac{dU}{dx}$$ Letting $\frac{dU}{dx}=v$ $$-x \frac{dv}{dx}=(ax+b)v$$ Rearranging $$-\frac{1}{v} dv=\left(a+\frac{b}{x}\right)dx$$ $$ -\int(\ln{v}) dv= \int \left(a+\...
Tosh's user avatar
  • 190
2 votes
Accepted

Expectation of the negative exponential utility function for a Grossman and Miller model

Deriving the expected utility comes from an application of the moment generating function of a Normal random variable: Let $U(W)=-e^{-\lambda W}$ and $W=x \cdot \bar{p}$ where $\bar{p} \sim N(\mu, \...
Pleb's user avatar
  • 4,231
1 vote

How to compare mean-variance-skewness-kurtosis portfolios obtained by expected utility maximization?

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 ...
Pontus Hultkrantz's user avatar
1 vote
Accepted

Closed Form Solution for Implied Risk Aversion with Two Assets under Quadratic Utility

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: $$ \...
Kermittfrog's user avatar
  • 6,535
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 ...
Dave Harris's user avatar
  • 4,369
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 ...
Ezy's user avatar
  • 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 (...
phdstudent's user avatar
  • 8,041
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 ...
Andrew's user avatar
  • 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. ...
math's user avatar
  • 1,718

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