The tag has no usage guidance.

learn more… | top users | synonyms

1
vote
1answer
44 views

Proving function is convex argmin

How can I show that the following function is convex in which Z is a random variable? $$\rho(Z)=\frac{2}{3}\mathrm{argmin}_{t}\{t+10\mathbf{E}[Z-t]_{+}\}+\frac{1}{3}\mathrm{argmin}_{t}\{t+5\mathbf{E}[...
0
votes
1answer
32 views

Mean residual life function limits

In my paper about mean residual life functions and heavy tails I've come across the examples listed in the picture below. http://i.stack.imgur.com/OnklD.png source (page 124/125): http://www.mi.uni-...
0
votes
1answer
60 views

A level continuously paying annuity pay 1500 each month. Find the present value

Here is the full question: A level continuously paying annuty pays $\$ 1500$ each month for eight year. The force of interest is $\delta(t)=\frac{2t}{t^2+5}$ where time is measured in years. Find the ...
3
votes
1answer
60 views

$X<Y$ a.s. but $\mathrm{AV@R}_\alpha[X] = \mathrm{AV@R}_\alpha[Y]$

$\newcommand{\avar}{\mathrm{AV@R}_{\alpha}} \renewcommand{\Re}{\mathbb{R}}$Let $(\Omega, \mathscr{F}, \mathrm{P})$ be a probability space and define $\mathcal{Z}:=\mathcal{L}_p(\Omega, \mathscr{F}, \...
0
votes
0answers
15 views

Maximising returns Limiting Risk

This is probably a simple question/solution, but I'm no math expert. I'm looking into a Facebook group that provides bet to try and get up to 50k, you may have heard of it. The premise being that you ...
1
vote
3answers
57 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 ...
1
vote
1answer
24 views

Calculate the VaR at level alpha of the given CDF

I have to compute the mean value, the variance, the value-at-risk $\mathrm{V@R}_{\alpha}$ and the expected shortfall $\mathrm{ES}$ of a random variable with CDF $$ F(x) = \begin{cases} 1- (\frac{3}{...
2
votes
2answers
39 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. ...
0
votes
0answers
17 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
votes
1answer
47 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
votes
0answers
27 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%?) e....
1
vote
1answer
321 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 $SD(...
1
vote
1answer
140 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
votes
1answer
139 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) $\limsup_{x\to\infty}\frac{\...
1
vote
1answer
63 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
votes
1answer
187 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
votes
1answer
60 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
160 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
votes
1answer
157 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
78 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
vote
1answer
144 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
votes
1answer
463 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 bid,...
0
votes
0answers
55 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
vote
1answer
90 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
110 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
750 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)= P(...