# 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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### Is "extreme CVaR" (CVaR from extreme value theory) elicitable or conditionally elicitable with some other statistical mapping (like VaR)?

I am recently using deep reinforcement learning (DRL) for solving risk-averse markov decision processes (RA-MDP) using risk measures which are either elicitable or conditionally elicitable (as in the ...
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### 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 Proof $I(a)=\int ^{}_{s} {a}dv=\int ^{\infty }_{0} {v}\left \{ {s\in S|a(s)≥\alpha } \right \} d\alpha ,a\in {B}_{+}\left ( {S,\Sigma } \right )$

Let $\Sigma$ denote a non-empty algebra of subsets of a set S, let B(S, $\Sigma$) denote the set of bounded, real valued, $\Sigma$-measurable functions on S, and let v denote a monotonic real ...
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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 ...
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### Risk measures and Bellman's principle of optimality in the context of risk-sensitive MDPs

I'm learning about finite-horizon risk-sensitive Markov Decision Processes (MDP) in the context of stochastic shortest path problems. In a nutshell, instead of finding a policy that minimizes the ...
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### 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 ...
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### Distribution of $X(T)$ where $T$ is the time of ruin.

Given a ordinary renewal process $$X\left(t\right)=u+ct-\sum^{N\left(t\right)}_{i=1}{Y_i},\ \ \ t\geq{0}$$ where $u\geq 0$ is the initial surplus, $c$ represents the insurer’s premium income per ...
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### Need help to understand how an individual model can be transformed into a collective one

Can someone help me to understand the following section which is intended to show that the individual model is a special case of the collective model. (To be precise: From a given individual model we ...
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### 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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### 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 ...
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### Analyzing a Gambling Race Paradox

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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### 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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### Compound Poisson models with completely monotone claim sizes

Assume that the free surplus of an insurance company at time t is modeled by \begin{equation} R(t)=u+ct-\sum_{k=1}^{N(t)}X_k \end{equation} where u is the initial surplus, the stochastic process N(t) ...
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### Risk Management System

I am attempting to create a hypothetical risk management system for crypto trading based on the size of my portfolio. I have initial conditions of 200 dollars of initial capital and 200 dollars per ...
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### What is a good introductory book on mathematical risk theory?

I'm looking for a book that introduces the following concepts and illustrates them with examples and exercises: Risk measures (Value at Risk, Expected Shortfall, distortion risk measures, and more) ...
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