0
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0answers
26 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 ...
0
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0answers
25 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 ...
2
votes
1answer
28 views

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. ...
0
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0answers
71 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 ...
5
votes
1answer
206 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 ...
1
vote
1answer
87 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 ...
1
vote
1answer
497 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 ...
0
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1answer
1k 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 ...
0
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1answer
497 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 ...
2
votes
1answer
383 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 ...
0
votes
0answers
212 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 ...
0
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1answer
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 ...
0
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0answers
162 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) ...
1
vote
1answer
153 views

Normal distribution probability

just a quick question dealing with probability. The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal ...
5
votes
1answer
227 views

Measure of value of resources in a competitive game

Let we have a competitive survival game in which a player has choice between different resources to earn. The question here is which resource should he prefer to maximize the chance of survival. I ...