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Time-at-risk
Time at Risk (TaR) is a time-based risk measure designed for corporate finance practice. TaR represents certain quantile for a given probability distribution, so is similar to Value at Risk (VaR). However, TaR measures risk amount as time(time until an adverse event) rather than value (loss amount). Definition and examples Mathematical definition of TaR is same as that of VaR. However, value-based random variable is replaced with time-based one, and given time-horizon is replaced with given finance structure. Examples comparing VaR and TaR are as below. *“An insurance company's 90% VaR is 10 million dollars for 1-year insurance risk.” : This means it is 90% probability that insurance claim payout would be below 10 million dollars; so if the insurer has accumulated 10 million dollars in cash, it would be 90% safe. *“An insurance company's 90% TaR is 3 years for liquidity risk under current finance structure.” : This means it is 90% probability that net liquid assets(= ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Risk Measure
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the downside risk, risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator (economics), regulator. In recent years attention has turned to coherent risk measure, convex and coherent risk measurement. Mathematically A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns. The common notation for a risk measure associated with a random variable X is \rho(X). A risk measure \rho: \mathcal \to \mathbb \cup \ should have certain properties: ; Normalized : \rho(0) = 0 ; Translative : \mathrm\; a \in \mathbb \; \mathrm \; Z \in \mathcal ,\;\mathrm\; \rho(Z + a) = \rho(Z) - a ; Monotone : \mathrm\; Z_1,Z_2 \in \mathcal \;\mathrm\; Z_1 \leq Z_2 ,\; \mathrm \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |