Effective risk management truly depends to a large extent on the use of probability concepts. Particularly, probability concepts are used to estimate:
(i)the average number of losses or average aggregate amount of losses from specified peril in a given period.
(ii) the variability around these averages of the number of losses or aggregate amount of losses per period.
(iii) from points(i) & (ii) the likelihood that the number of losses or the aggregate amount of losses in a given period will exceed a specified number or amount.
In addition to helping in estimating average losses and chances of losses of varying degrees of severity, the probability concepts are of great value in other phases of the risk management process, such as analysing accident frequency and severity rates, determining the reasonableness of insurance premiums or the adequacy of reserves established for risk retention, and selecting alternative risk management techniques on the basis of the probable impact on an organisation’s profits and efficiency.
The collection and interpretation of information forms are important part of risk management function. Interpretation of data involves the use of procedures and probability concepts.
Data is usually represented in the form for frequency distribution. These can further be reduced to summaries. Probability is the related frequency with which a specified novel is can be expected to occur in the long run. For example, in a given number of tosses, a coin can come up with as many number of heads as tails.
Such probabilities are expressed in fractions, or percentages, i.e ½ or 50%. The probabilities associated with the coin tosses can be developed theoretically. They are called prior to experience or a priori. On the other hand, the probability of a specified car to be stolen in a year may be 1/99 or 1.01%.
The probability that a car will be stolen within the year cannot be deduced theoretically. It must be estimated by studying a sample of cars and seeing what proportion were stolen. These probabilities based solely on historical data are often described as empirical or experimental probabilities.
A probability distribution is a presentation of all possible outcomes of a particular set of circumstances and the probability of each outcome.
Most probability distributions encountered in risk management are not symmetrical. Distributions of numbers of losses, or amounts of losses, in a given time period tend to peak at relatively low probability of large number of losses.
Sometimes, the probability distribution may suggest a degree of precision, however, when the loss data is limited, there may be a short series of loss figures from which to estimate the loss probability. If this data is definitely distinctive, then it cannot be applicable to general forecasting, or detailed probability distribution.
The probability distribution illustrates two characteristics,
(i)Central tendency or clustering and
(ii)Dispersion or variability, which are vital tools in forecasts of average levels of losses and excessive losses, both crucial forecasts in risk management.
(i)Central tendency or clustering – most probability distributions tend to cluster around a film by the numbers are particular value, which may not be in the middle of the range of the possible distribution covers.
The widely used methods of calculating the value are the arithmetic mean, the median, and to the mode of a distribution.
The arithmetic mean is the more precise name given to average, which is the sum of the items divided by the number of items.
The only difference in calculation of arithmetic mean of a probability distribution is that instead of dividing by the number of items, each item in the probability distribution is multiplied by its respective probability and the sum of these products is divided by the sum of the probabilities.
Because these arithmetic means do represent long run average expectations, the arithmetic mean of a probability distribution is usually referred to as the expected value of that distribution.
The median of a distribution is the value in the middle, i.e the value around which the number of lower observations equals the number of higher observations.
To find the median of a probability distribution, the procedure is to locate the value below (or above) which 50% of the observations fall. This is done by summing the cumulative probabilities in the distribution and finding the value associated with the required cumulative probability.
The mode of distribution is the only single value which is most likely to occur.
(ii) Dispersion or degree of variability from the point around which. The lesser the dispersion, the closer would be the result with the breakdown of the organisation and visual of a Roman who will the original value, and hence lesser risk in prediction of the result. There are usually two methods of deviation, standard deviation, and coefficient of variation.
The principal contribution of probability is to make the problem more manageable by focusing only on certain specific questions. Probability distributions can also help determine whether to accept a deductible. The Risk Management specialist can determine :
(i) Whether the firm is willing to accept the probability that the retained losses will exceed the premium saved by purchasing the deductible.
(ii) He can determine whether the elimination of the worry about the losses is worth paying the amount by which the premium savings exceed the average retained loss.
Probability distributions can also determine whether the effect of loss prevention measures on the potential losses faced by the firm is worth the involved expenditures.
