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3answers
45 views

Basic math, Confusion working out chance of failure.

While I am quite technical, I am not a mathematician. So please be forgiving if this question seems overly simple. My probability abilities left me long ago. I have a problem which I was arrogant ...
0
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0answers
11 views

Calculate the VaR at level alpha of the given CDF

I have to compute the mean value, the variance, the $Var$ and $ES$ of the $CDF$ $F(x)= 1- (\frac{3}{2x})^{-3}$ if $x\geq 3$ $F(x)=0$ if $x< 3$ The mean and variance I have computed, but what ...
2
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2answers
29 views

Convex risk measures

What is the intuitive explanation for convex risk measures represented as: $$\rho(X)=\sup_{P\in Q}\{E_{P}(-X)+\alpha(P)\}$$ where $\alpha(P)$ is a penalty function depending on the plausibility of P. ...
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0answers
16 views

Formulating simple games as Bayesian problems

Say you are in a game where every win doubles your money and every lose halves. You can walk away any time with the money you have by giving up? The rules of game is every step a problem is posed ...
0
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1answer
36 views

Using risk aversion

I'm trying to figure out what the non-stochastic equivalent payment is for someone who is risk-averse. Suppose we have a lottery that pays out\$100 with probability one half and \$0 with probability ...
0
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0answers
26 views

X% per turn over Y turns? Is my working out correct? risks and probabilities.

4% per turn * (over the course of) 25 turns. e.g. 1 Person $\alpha$ let's call him bob. Bob a 4% chance of winning something every day for 25 days. Whats the chance of him winning? (about 100%?) ...
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0answers
27 views

Is it a Risk-averse utility function?

I'm a little unsure whether this utility function represents a risk-averse attitude, while it's not wholly concave: Would you define it as both risk-averse and risk-neutral as it seems to have ...
0
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0answers
38 views

Decisions with Probabilities - application

A company has to decide whether to manufacture a product at its plant or purchase from a supplier. The resulting profit depends on the demand for the product. The estimated profit is shown below: ...
1
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1answer
251 views

Tangent portfolio weights without short sales?

Consider a mean-variance investor in a world with a risk-free asset. Let $R_f>0$ be the return of the risk-free asset, $\mathbb{E}(R_i)>R_f$ the expected return of the risky asset $i$ and ...
1
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1answer
93 views

Portfolio Theory - Finance Riskless Assets Return

A market consists of two risky assets and one riskless asset. Asset 1 has a return of 8% and a risk of 10%. Asset 2 has a return of 16% and a risk of 30% The correlation between the returns of the two ...
8
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1answer
129 views

Heavy-tailed distributions

I have encountered the following two definitions of heavy-tailedness (right tail) for a $[0,\infty)$-valued random variable $X$ satisfying $\mathbb{E}[X]<\infty$: (i) ...
1
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1answer
59 views

Algorithm for risky investments in banks

I made the following programming question on stack overflow but the users said it was more of math question. Here it is. Situation You start with a fixed amount of money, take it as $\$1000$. You ...
0
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1answer
154 views

Calculate single “battle” outcome odds for RISK

I am trying to reproduce the values in this odds ratio table from Wikipedia. For all those unfamiliar with RISK, this is a game where units fight against each other via the roll of the dice: The ...
0
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1answer
58 views

How to find the expectation value?

Suppose that an insurer has an exponential utility function $u(x)=−2e^{-2x}$. What is the minimum premium $P^{-}$ to be asked for a risk X? After solving this we reached the following, So,only ...
3
votes
1answer
128 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I've asked the same question at the Quantitative Finance StackExchange. Consider the following example: "As a risk-averse consumer, you would want to choose a value of x so as to maximize expected ...
0
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1answer
137 views

Markov chains example

Your exam could be marked with a range of possible grades, simplified as on the following state diagram: To begin with the chances are that you will pass with a standard result. Each 45 minutes ...
1
vote
1answer
70 views

What is the minimum Premium to be asked for a risk X?

Suppose that an insurer has an exponential utility function $u(x) =-2e^{-2x}.$ What is the minimum premium $P^{-}$ to be asked for a risk X? I got some hint for this, but I could not understand ...
1
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1answer
117 views

Question about the risk analysis.

In the above one can see the detail of this question, I am beginner in this kind of mathematics. I will be very greatful if any one can help me to solve them.
9
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1answer
428 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 ...
0
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0answers
52 views

Calculate risk that occurs p% of a time

In a search of a way to calculate variance for risk management I found the following formula (n1, n2, n3 are data points): ...
1
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1answer
85 views

Risk and probability: Is there always infinite risk?

If there are an infinite number of events with a cost (risks), and total Risk is calculated by the sum of all individual risks multiplied by their probability, does everything have an infinite risk ...
0
votes
1answer
109 views

Expected value of OR gate

Suppose a system such as A+B where + means OR. Suppose A and B are identical. Each event obeys exponential distribution with mean $\lambda$. What is the mean $\lambda_{\text{System}}$ for the whole ...
1
vote
0answers
27 views

Dominance relation with different confidence intervals: why not always acting like a strict poset?

I have noticed that a dominance relation acts like a strict poset with the confidence interval equal to 0 but very differently with non-zero confidence intervals. For example, 1D2 and 2D3 always ...
1
vote
1answer
600 views

PRA: Rare event approximation with $P(A\cup B \cup \neg C)$?

The rare event approximation for event $A$ and $B$ means the upper-bound approximation $P(A\cup B)=P(A)+P(B)-P(A\cap B)\leq P(A)+P(B)$. Now by inclusion-exclusion-principle $$P(A\cup B\cup \neg C)= ...