Questions tagged [risk-assessment]

For questions about risk assessment, a systematic process of evaluating the potential risks that may be involved in a projected activity or undertaking.

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Isoelastic utility functions, how to calculate risk boundaries.

I am trying to replicate a calculation I found in a paper that calculates the level of risk aversion for an individual to choose one option over the other, but I am struggling to solve it. Ideally, ...
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Find the trivial interval for fair prices

Suppose there is a risk-free asset with $r^0 = 5$ and $2$ risky assets with $E r^1 = 8, \sigma^1 = 5, E r^2 = 20, \sigma^2 = 20, \text{corr}(r^1, r^2) = 0$. What is the maximum average profit and ...
1 vote
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Calculating the RRR

I want to calculate my Risk-Reward-Ratio to pipe it into an equity simulator. The risk is calculated by dividing the reward by the risk. I also need the number of iterations and the hit rate to get ...
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Equality case in the subadditive property of Expected Shortfall

If $Z_1$ and $Z_2$ are two $L^1$ real-values random variables, it is well known that $ES_\alpha(Z_1+Z_2) \le ES_\alpha(Z_1) + ES_\alpha(Z_2)$ for any $\alpha \in (0,1)$ However, what about the ...
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How do I prove monotonicity of risk measures?

Assume I have a risk measure, that is a functional $R:L^\infty(\Omega, F,P)\to \mathbb{R}$, that applies to random variables $X:\Omega\to\mathbb{R}$. Assume the functional satisfies the following ...
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Proof that $VaR_c(L)=(\Phi^{-1}(\frac{c+1}2))^2$

The loss $L$ has the $\lambda_1^2$ distribution, i.e. the distribution of the random variable $X^2$, where $X$ has a standard normal distribution. Proof that $VaR_c(L)=(\Phi^{-1}(\frac{c+1}2))^2$, ...
• 353
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How are the two statements same mathematically? [closed]

I am doing a data course on statistics and in one of the questions, they're suggesting that the statements given below are mathematically the same. I disagree. Can they be mathematically proven to be ...
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What is the occupation measure for constrained risk-averse markov decision processes with only expectation constraints (no risk constraints)?

I have formulated my optimization problem as a constrained risk averse markov decision process. In my solution methodology I want to use occupation measure of the formulated problem. I have searched ...
23 views

Probability Risk Evaluation

I have a batch of 50 items. There is an inspection pass/fail criteria and 3 out of 50 failed inspection. How do I determine if I pick 10 random items from this batch of 50 the probability %age that I ...
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How to find a bayes risk

Let $X$ follows a normal distribution with parameters $\theta$ and $\sigma^2$. Let a prior for $\theta$ be a Normal distribution with parameters $\mu$ and $b^2$. How can I find the Bayes risk of this ...
37 views

I don't know where I'm going wrong in calculating the expected replacement cost

This is the question: Suppose the probability a plant is destroyed in year 1 is 2% and the probability a plant is destroyed in year 2 assuming it was not destroyed previously is 4%. When the plant is ...
1 vote
895 views

How to calculate Relative Risk Reduction and Absolute Risk Reduction?

In this guide they try to teach how to calculate relative and absolute risk reduction. Problem: My understanding of the formulas leads to different result than they say. Data and results given ...
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1 vote
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Correctly comparing the risk posed by a single task to the risk posed by a repetitive task

I have been told that I have come up with a comparison which statistically doesn't make sense. But no one has told me how to correct the comparison. Although I believe it is related to an increased ...
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1 vote
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IB Extended Essay Research Idea Inquiries

I am currently a senior in the IB program at my school and I have to write a full-length paper on mathematical research I have conducted. My idea for my paper was to create a gaussian function (normal ...
1 vote
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In https://sites.math.washington.edu/~rtr/papers/rtr206-RiskTutorial_INFORMS2007.pdf, Rockafellar defines a coherent risk measure in the following way: $\rho : \mathcal{L}^2(\Omega, \mathcal{F}, P) \... • 101 1 vote 0 answers 108 views Discrete random walk/risk process characterized by a step distribution with a heavy tail and a mean existing only as a Hadamard finite-part integral This question is an attempt to make more precise two previous questions of mine on another SE (this and this). The random walk/risk process of interest Consider the following discerete process. Let$n=...
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Suppose a number of players are given $100$ points each, and repeatedly engage in a gamble having positive expected value, with the goals of being the first player to reach $100000$ points. Solving ...
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Find the sample size $n$ for a stratified sampling method

Let’s say we have a finite population $N=5000$.We have divided the population into 5 subgroups according to a risk characteristic “very low risk”,”low risk”,”medium risk”,”high risk” and “very high ...
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Insurance statistics book

Am am looking for a book on insurance statistics. The problem is that there are a lot of googleable variants that it is difficult to decide which one is good and which ones are better in good ones. ...
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Question about the mean excess loss function.

I'm new to this risk thing. I am trying to obtain the mean excess loss function evaluated at a point for the following Pareto distribution: $F(x)=1-(\frac{\theta}{x})^{\alpha}$ The excess loss ...
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1 vote
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Prove that $E_θ(θ-\frac{X}{100})^2 = \frac {θ(1-θ)}{100}$

$X \text {~} Binomial(100,θ)$, $δ(X)=\frac {X}{100}$, $g(θ)=θ$ and the loss function is given by $L(θ,d)=(θ-d)^2$. The risk function for δ is $R(θ,δ) = E_θ(θ-\frac{X}{100})^2 = \frac {θ(1-θ)}{100}$ I ...
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Example of a risk measure that is not law-invariant

In some theorems about risk measures, the property of law invariance is required. Let $\mathcal{Z} = \mathcal{L}(\Omega, \mathcal{F}, P)$. A risk measure $\rho\colon \mathcal{Z}\to \mathbb{R}$ is law ...
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Optimization of stop-loss contract with respect to CVaR.

I'm trying to figure out where my mistake is. I'm trying to optimize a parameter for a stop-loss type contract with respect to conditional value-at-risk. I have attempted to differentiate with respect ...
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Philosophically motivated risk metrics

During a random process over a sample space $\Omega$, an agent incurs a cost (say, in money) given by a random variable $Z:\Omega \rightarrow R$, which is determined by the agent's action. The agent ...
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