What is subadditive property?
In mathematics, subadditivity is a property of a function that states, roughly, that evaluating the function for the sum of two elements of the domain always returns something less than or equal to the sum of the function’s values at each element.
What does Countably subadditive mean?
A set function is said to possess countable subadditivity if, given any countable disjoint collection of sets on which. is defined, A function possessing countable subadditivity is said to be countably subadditive.
Is VaR sub an additive?
VaR is known to be subadditive in some special cases such as when asset returns are normally distributed in the area below the mean, or more generally for all log-concave distributions, see Ibragimov (2005).
What does a Subadditive cost function entail?
2.14 Subadditivity of the Cost Function
For a multiple-output firm, Subadditivity of the cost function holds when the cost of joint production is less than (or equal to) the cost of separately producing each output.
Why VaR is not coherent?
In other words, VaR is not a “coherent” measure of risk. This problem is caused by the fact that VaR is a quantile on the distribution of profit and loss and not an expectation, so that the shape of the tail before and after the VaR probability need not have any bearing on the actual VaR number.
What does a subadditive cost function entail?
Is Outer measure subadditive?
(2) Outer measure is countably subadditive but is not countably additive, and indeed there are disjoint sets A and B such that m∗(A ∪ B) < m∗(A) + m∗(B).
Why is value at risk not Subadditive?
It is important to realise that VaR is not always subadditive because often people take two VaR and add them together and say “well this is an upper bound”. Since this isn’t true it can cause wrong decisions to be made.
How are natural monopolies created?
Key Takeaways. A natural monopoly is a type of monopoly that arises due to unique circumstances where high start-up costs and significant economies of scale lead to only one firm being able to efficiently provide the service in a certain territory.
Why is VaR not additive?
VAR is not additive. This means the VAR of individual stocks does not equal to the VAR of the total portfolio. It is because VAR does not consider correlations, and thus, adding may result in double counting. There are various methods to calculate VAR, and each method gives a different result.
Is VaR a convex risk measure?
CVaR is a so-called “coherent risk measure”; for instance, the CVaR of a portfolio is a continuous and convex function with respect to positions in instruments, whereas the VaR may be even a discontinuous function.
What is the difference between outer measure and measure?
So, a measure is an outer measure with a domain that no longer consists of all subsets of a space X but is defined on a sigma-algebra of subsets of X, but which is countably additive instead of countably subadditive. The monotonicty property (3) of an outer measure is implied (see example below).
Why do we measure outer?
The purpose of constructing an outer measure on all subsets of X is to pick out a class of subsets (to be called measurable) in such a way as to satisfy the countable additivity property.
What are the benefits of natural monopolies?
What are the Advantages of Natural Monopoly?
- Natural Monopoly Prevents Duplication. Since the sole efficient provider of goods and services is one, the possibility of duplicate products decreases.
- Lower Prices.
- Companies can conduct better research.
- High Profits are the main advantages of Natural Monopoly.
- Large Output.
Why is a natural monopoly beneficial?
A natural monopoly is allowed to exist and flourish in the market because it can supply specific service or product at a cost that is very lower than any potential rival can and that too in bulk to meet the demand of an entire market.
What is the limitation of VaR?
Limitations of Value at Risk
Calculation of Value at Risk for a portfolio not only requires one to calculate the risk and return of each asset but also the correlations between them. Thus, the greater the number or diversity of assets in a portfolio, the more difficult it is to calculate VaR.
Is VaR minimum or maximum loss?
Value at Risk (VAR) calculates the maximum loss expected on an investment over a given period and given a specified degree of confidence.
What does a negative VaR mean?
A negative VaR would imply the portfolio has a high probability of making a profit, for example a one-day 5% VaR of negative $1 million implies the portfolio has a 95% chance of making more than $1 million over the next day.
Why do we need outer measure?
How do you prove an outer measure?
Mod-03 Lec-10 Outer measure and its properties – YouTube
Why outer measure is not countably additive?
The outer measure satisfies all the axioms of a measure except (countable) additivity. However, it is countably additive when one restricts to at least the Borel sets, as this is the usual construction of Borel measure. This result is roughly contained in the Caratheodory Extension theorem.
What are the characteristics of a natural monopoly?
Generally speaking, natural monopolies are characterized by steeply declining long-run average and marginal-cost curves such that there is room for only one firm to fully exploit available economies of scale and supply the market.
What are examples of natural monopolies?
A natural monopoly will typically have very high fixed costs meaning that it is impractical to have more than one firm producing the good. An example of a natural monopoly is tap water.
…
Examples of Natural Monopolies
- Gas network.
- Electricity grid.
- Railway infrastructure.
- National fibre-optic broadband network.
Which is the best example of a natural monopoly?
The case of tap water can be an example of a natural monopoly. It makes sense to have only one company providing a network of water pipes and sewers because the setting up of a national network of pipes and sewage systems entails very high capital costs.
Is natural monopoly good or bad?
In economics a natural monopoly is said to exist when a single business, rather than numerous competing businesses, is the most efficient producer of any good or service.