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1answer
27 views

Why do we assume quadratic utility in portfolio theory?

In my text (Investments by BKM), the investor's mean-variance utility (given as $U = E[R] - \frac12A\sigma^2$) is stated to be the objective function we wish to maximize. Upon further digging, it ...
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0answers
18 views

Asset weights in asset allocation

I am trying to solve an asset allocation problem by approximating the expected utility of a portfolio. I am using the following formula: $E_t [U(1 + w_t' r_{t+1} + w_{ft} r_{f, t + 1})] = m_{1,t+1} - ...
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0answers
24 views

Embedding the naive portfolio into economic decision theory

I am trying to gain some insights about the vast literature of portfolio optimization and I hope to get some help when it comes to embed the most standard allocation strategies into a coherent ...
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0answers
27 views

Approximating the conditional expectation in simulations

I am simulating stock returns, which are governed by the following equations $r_t = \mu + \delta r_{t-1} + \sigma_t z_t$ $\sigma^2_t = \omega + \alpha \varepsilon_{t-1}^2 + \beta \sigma^2_{t-1}$ ...
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2answers
51 views

How to arrive at expectation of negative utility function via Taylor series expansion

I'm attempting to follow an author's steps in an argument and having trouble seeing how Taylor series expansion can be applied to give the stated result. The scenario is as follows. The mid price ...
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0answers
17 views

Reference Request: Portfolio Optimization Conditional on downside threshold

Under a standard portfolio optimization framework we have some idea of a predictive return distribution $r_{t+1}$ and a Utility function $U(r)$, in the best case in a 'nice' form (differentiable ...
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2answers
165 views

Utility Theory and portfolio optimization - Proof of a lemma

I have a question on the following problem from chapter 9 of D. Luenberger, Investment Science, International Edition: (Portfolio Optimization) Suppose an investor has utility function $U$. ...
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1answer
169 views

Utility Theory - How to show that this exponential utility function is wealth-independent?

I have a question on the following exercise from chapter 9 of D. Luenberger, Investment Science, International Edition. Exercise 2 (Wealth Independence) Suppose an investor has exponential ...
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1answer
129 views

Utility Theory - Certainty equivalent approximation formula derivation

I have a question on an exercise from chapter 9 of D. Luenberger, Investment Science, International Edition, where I suspect there may be a typo. Exercise 8 (Certainty approximation) There ...
1
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1answer
65 views

Investor choice problem

Guys I'm stuck with a problem... Consider the portfolio choice problem of a risk-averse individual with a strictly increasing utility function. There is a single risky asset, and a risk free asset. ...
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2answers
43 views

Expected Utility

We know that under certainty, any increasing monotone transformation of a utility function is also a utility function representing the same preferences. Under uncertainty, we must restrict this ...
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0answers
55 views

Financial theory

Ok guys, I'm studying from Danthine and Donaldson - Intermediate Financial Theory. The book itself doesn't have a lot of worked examples, and I'm lacking the basics for understanding some concepts ...
0
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1answer
70 views

Expected Utility and $\log$

I've just started reading about expected utility and utility functions and have the following question. $\textbf{Question:}$ An investor has an initial wealth of 100 and a utility function of the ...
1
vote
1answer
32 views

convention in borrowing money in a multiperiod model

I have a question concerning the idea of consumption in multi period. The following is given $$C_1=W_0-xS_1+B$$ $$C_2=xS_2-BR$$ where $W_0$ is initial wealth $x$ is the weight on an asset with ...
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1answer
51 views

Implicit relation between risk and reward

I want to differentiate w.r.t. $\sigma^2$ the following equation $u'(Y)\mu$ + $\frac{u''(Y)}{2}$$(\sigma^2 + \mu^2) = 0$ where we can consider $\mu$(reward) as an implicit function of $\sigma^2$(risk) ...
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0answers
48 views

Comparing cost of two alternative given their distribution

I have distribution for cost of two alternative through Monte Carlo simulation. The distributions are not normal. Given the benefit of the two alternatives is the same but ungiven, I want to choose ...
3
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2answers
346 views

Validity of CAPM

I came across some literature regarding "Framing Theory" or "Prospect Theory", and the validity of CAPM. I was wondering if you could shed some light on a few questions I have in this regard: ...
4
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1answer
326 views

Why maximize expected growth rate?

It seems to me that the optimality of the Kelly Criterion relies on the assumption that it is in an investor's best interest to maximize his portfolio's expected growth rate. Why would he care what ...
5
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1answer
217 views

Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?

Or simply: why do we call equivalent martingale measures as risk-neutral measures? In the utility or game theory, when we consider a person's preferences to certain outcomes, we often deal with the ...
4
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2answers
113 views

Critique against consumption-based asset pricing theory?

I find asset pricing theory very vague and full of assumptions, especially the consumption-based modern theory. In its essence, the theory states that asset prices depend on the covariance between ...
1
vote
1answer
267 views

Why are indifference equations in mean-variance portfolio theory convex shaped

As the title suggests why is the indifference equations in mean variance portfolio theory convex shaped? Indifference Equation: https://en.wikipedia.org/wiki/Indifference_curve A graph:
4
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1answer
151 views

Estimating investor's utility from the trades data

Is it possible to infer investor's utility function from the set of decisions she is making? Let's assume for simplicity that the market consists of a single traded asset whose return distribution is ...
3
votes
1answer
221 views

Desired portfolio volume

I am working on a toy model, in part of which an investor has to decide (based on some utility theory) how much money to invest in a given portfolio. For simplicity, assume that the portfolio is ...
5
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2answers
409 views

Does a coherent risk measure satisfy the four axioms of von Neumann–Morgenstern?

What is the relationship between the axioms of Artzner et al (1999) for coherent risk measures and the axioms of von Neumann-Morgenstern (1944) for the expected utility theory?
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2answers
99 views

Function that best describes intensity of human/(group of humans) emotions?

Let me give you couple of examples. You're at a dinner and you order something. You could say: "It's OK" "It's good" "It's great" "It's fantastic" "I've never ate something this good" "Goodlike" ...