By M. Khoshnevisan, S. Bhattacharya, F. Smarandache

ISBN-10: 1931233772

ISBN-13: 9781931233774

The aim of this publication is to use the substitute Intelligence and keep an eye on platforms to assorted genuine versions. it's been designed for graduate scholars and researchers who're energetic within the purposes of man-made Intelligence and keep an eye on platforms in modeling. In our destiny study, we'll tackle the original features of Neutrosophic common sense in modeling and knowledge research.

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50) To see how the expected change in investor’s equity goes up with an increased upside potential we will double the possible up movement at each of the next two stages while keeping the down movement unaltered. This should enable us to account for any possible loss of investor utility by way of the cost of using a portfolio insurance strategy. 800 Expected excess equity Figure 1 The utility function as obtained above is convex in probability space D, which indicates that the protective strategy can make the investor risk-loving even when the market is expected to move in an adverse direction, as the expected payoff from the put option largely neutralizes the likely erosion of security value at an affordable insurance cost!

Repeated simulations have shown that the investor would be considered extremely unlucky to get an excess return less than the minimum excess return obtained or extremely lucky to get an excess return more than the maximum excess return obtained under each of the event spaces. Hence, the maximum and minimum expected excess equity within a particular event space should correspond to the lowest and highest utility indices and the utility derived from the median excess equity should then naturally occupy the middle position.

E. 23722. These defining ranges as evaluated above will however depend on the parameters of the utility function and will therefore be different for different investors according to the values assigned to his or her utility indices corresponding to the expected excess equity. 44 In general, if we have a parabolic utility function u (x) = a + bx – cx2, where c > 0 ensures concavity, then we have u’ (x) = b – 2cx and u’’ (x) = -2c. The Arrow-Pratt measure is given by λ (x) = 2c /(b–2cx). Therefore, for λ (x) ≥ 0, we need b > 2cx, thus it can only apply for a limited range of x.

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Artificial Intelligence and Responsive Optimization by M. Khoshnevisan, S. Bhattacharya, F. Smarandache


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