# Tagged Questions

41 views

### Calculating the chance of something happening over and over again

I'm trying to calculate the probability, and potential cost on society, of people returning to homelessness after going through the system one, two, or several more times. Let's say that someone who ...
47 views

### Conditional and unconditional variance in ARMA processes

How can I compute the conditional and unconditional variance of $x_t$ given its past if $\{x_t\}$ is an ARMA$(p,q)$ process. I'm literally struggling over that. Cheers
73 views

### Von Neumannâ€“Morgenstern independence axiom vs. Savage independence theorm

Von Neumannâ€“Morgenstern independence axiom: Savage independence theorem: What is the difference between the two? I'm think Von Neumann is talking about the prizes (outcomes) and Savage is talking ...
103 views

### The Historical Importance of Keynes' A Treatise on Probability

A visiting speaker in Economics recently happened to mention that John Maynard Keynes' A Treatise on Probability revolutionized probability theory. I have not heard any such claim before and it struck ...
46 views

### Put-Call-Parity of Asian Options

I could need some help with deriving the put-call-parity for asian options. Let $S_t$ be the price of the underlying asset at time $t$ and set $Y_t = \int_0^t S_t dt$. Then the payoff of an asian ...
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### Arbitrage opportunity for call price set on avarage

I have the following problem. Let C(K) be the market price of a Option Call with respect to the strike K. Let $C(100) = \frac{C(110)+C(90)}{2}$, then show that there exists an arbitrage opportunity. ...
124 views

### Computing the certainty equivalent for the lottery of infinite expected value

How can I compute the certainty equivalent for the lottery for someone whose Bernoulli utility function is $u(x)=\frac{x^{1-\gamma }}{1-\gamma }$ where $0< \gamma < 1$? Also, how much would the ...
261 views

### Modelling risk when market making

I'm interested in learning about algorithmic trading, particularly in bitcoin. Looking at this chart, I can see that I could simultaneously offer a bid that was slightly higher than the highest ...
89 views

### Properties of concave,two-parameter function

I already showed that the function $\psi(\mu,\sigma)=\mathbb{E}U(X)$ is concave in $(\mu,\sigma)$, where $X$ is normally distributed with mean $\mu$ and variance $\sigma^2$. $U$ is a nice concave ...
583 views

### Mean preserving spread vs higher variance

In the Wikipedia article for mean-preserving spread, the following is claimed without citation: If B is a mean-preserving spread of A, then B has a higher variance than A; but the converse is not ...
2k views

### Can someone explain what plim is?

In my Introductory Econometrics class we discussed a concept of "plim" or "probability limit. I'm not sure what this means though and my professor doesn't explain it well at all. Can someone tell me ...
545 views

### bounding the the expected value of the maximum of two random variables

Consider two standardized random variables $x$ and $y$, and define a function $g(x,y)=E[max(x,y)]$ where $E$ is the expected value operator. My question is finding the upper and lower bounds of ...
427 views

### Solving a Maximum Likelihood Estimation with an exponential distribution

I need someone's insight on applying a MLE for an exponential distribution. In a finance paper, I have the following: $\displaystyle d_i \sim \frac{\epsilon_i}{\lambda_i}$ where $\epsilon_i$ is ...
237 views

### Monotonicity of expectation of a concave function of a random variable wrt the variance of the random variable

This is a question motivated from utility function. (See here and here.) I have been trying to develop some common sense in Economics by the way. Given a function $f: \mathbb{R} \to \mathbb{R}$ and a ...
64 views

### Probability of a new number given a set of $n$ previous numbers?

I have a set of numbers (each one corresponding to a payment made from the same person) and I would like to assign a probability value to a new specified number given that historical data. I've ...
182 views

### Understanding a Proof in Probability Theory

My question is pretty simple: I have two equations which are supposedly true (from a published paper) but I have no idea how to arrive at the solution myself. So it would be great if someone could a) ...