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.

Risk assessment is the determination of quantitative or qualitative estimate of risk related to a well-defined situation and a recognized threat (also called hazard). Quantitative risk assessment requires calculations of two components of risk (R): the magnitude of the potential loss (L), and the probability (p) that the loss will occur. An acceptable risk is a risk that is understood and tolerated usually because the cost or difficulty of implementing an effective countermeasure for the associated vulnerability exceeds the expectation of loss. "Health risk assessment" includes variations, such as risk as the type and severity of response, with or without a probabilistic context.

In all types of engineering of complex systems sophisticated risk assessments are often made within safety engineering and reliability engineering when it concerns threats to life, environment or machine functioning. The nuclear, aerospace, oil, rail and military industries have a long history of dealing with risk assessment. Also, medical, hospital, social service and food industries control risks and perform risk assessments on a continual basis. Methods for assessment of risk may differ between industries and whether it pertains to general financial decisions or environmental, ecological, or public health risk assessment.

Source: https://en.wikipedia.org/wiki/Risk_assessment

89 questions
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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, and an ask that was slightly lower than the…
Tom Busby
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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) $\limsup_{x\to\infty}\frac{\mathbb{P}(X>x)}{e^{-\lambda x}}>0$ for all…
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Existence of functionals on $L^0$

Studying a paper about risk measures by F. Delbaen, I bumped into this statement: Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space: if $\mathbb{P}$ is atomless, then there exists no functional $\rho:L^0\to\mathbb{R}$ such…
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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 chooses the action which minimizes its "risk",…
Frank Seidl
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Stochastic stability

In this book (p. 37, 43, 44) the notion of stochastic stability of a stochastic process is defined by the condition $$ \mathbb{E} \left[\sum_{j=0}^{\infty} \|x_k\|^2\right] < \infty.\tag{1} $$ It is shown that for Markovian switching systems of the…
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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 utility, i.e. Given actuarially fair insurance,…
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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. This is why I am asking here for sugestion. To be…
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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 $SD(R_i)$ the standard deviation of the return of the risky…
Star
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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 need help to solve the last step.
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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 properties It is monotonic: $X\geq 0 \implies…
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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 $VaR_c(L)=(\Phi^{-1}(\frac{c+1}2))^2$, where $\Phi$ is the cumulative distribution…
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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 many related databases and journals but cannot…
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Markov chain exercise 1

I have the transition matrix $$P= \begin{pmatrix} 1 & 0 & 0\\ 0 & 0 & 1\\ \frac14 & \frac14 & \frac12 \end{pmatrix}$$ and I have to determine the period of each state, compute $f_{2,2}{(n)}$ for each $n\geq 1$ and compute $p_2(X_n=3)$ I think…
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Reserve for Credit Loss

This is a regulatory way to calculate a reserve for credit loss. I want to interpret this formula. $$Lifetime\ Reserve=\frac{PD\times LGD\times EAD}{(1+i)}\left[\frac{1-(1-PD)^n}{PD}\right]-$$ $$\frac{PD\times LGD\times…
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