Abstract
In this paper, we shall validate the optimal payoff of an investment with an N-step utility function, [6, 7], such that H* is the payoff at time N in every possible state say 2n; in an N period market setting. Negative exponential, logarithm, square root and power utility functions were considered as the market structures change according to a Markov chain. These models were used to predict the performances of some selected companies in the Nigeria Capital Market. The estimates for models design parameters p, q, p', q' correspond to halving or doubling of investment. The performance of any utility function is determined by the ratio q: q' of the probability of rising to falling as well as the ratio p: p' of the risk neutral probability measure of rising to the falling.
Highlights
Portfolio management is all inclusive activity in our daily life
Material and Methods Data were collected randomly based on their performance from different key sectors for 236 days from some companies quoted in the Nigeria Capital Market; which include Custodian and allied insurance plc (CA), Dangote cement plc (DC), Fidson health-care plc (FD), First bank plc (FB), Honey-well Flour Mill plc (HF) and Mrs Oil Nig. plc (MRS)
Results were obtained for various models such as negative exponential model, logarithm model, square root model, and with power model being a generalization of square root model
Summary
Portfolio management is all inclusive activity in our daily life. For an example, one has got a particular amount of money and tries to use it in such a way that one can draw the maximum possible utility from the corresponding activities. The main drawback of this approach is the static nature of the problem: after the decision concerning the allocation of initial wealth to the different shares has been made at the beginning of the period, no further actions are allowed until the end of the initial portfolio is chosen, the investor's job is complete and his/her only feasible action is to watch the prices move without the possibility to intervene. This is an extreme oversimplification of reality and totally ignores the highly volatile behaviour and dynamic nature of prices. Continuous-time models offer more satisfying solutions to these problems
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