An alternative method to quantify risks (instead of expected loss) is as follows

Question

An alternative method to quantify risks (instead of expected loss) is as follows. If L represents a random variable associated with loss and E [middot] represents the expectation function, then instead of computing E[L], we can compute E [V(L)], where V (middot) is a function that increases greater than linearly. The rationale here is that we may want to model the "severity" of a loss to increase more than just linearly with loss. For example, the severity of losing one million dollars in a project is more than a million times that of losing one dollar. in the standard risk model, the expected loss is written as: E [L] = P_e times P_i times l_t where P_e is the probability of the risk event occurring, P_i is the probability of the impact, and l_t Element L is the total loss. Now, consider computing E [V(L)] as follows. First compute V (l_t), and then multiply this by the risk likelihood: E [V(L)] = P_e times P_t times V (l_t) (This method assumes that V (0) = 0.) Suppose we use V (l_t) = l^2_1? (square function of total loss) and we prioritize our losses according to E [V(L)] instead of E [L]. Specifically, we select a threshold for E [V(L)]. This corresponds to different threshold line on the risk map. What does this new threshold line look like? Illustrate this using a picture, contrasting it with the usual threshold line.

Explanation / Answer

Instead of a linear relation, quadratc relation exist. The product of Pe and Pi is a constant that is same in both linear and quadratic case. Let us consider this product as 1. The resultant graph will look as below

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