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A new model of capital asset management was developed under the assumptions of hyperbolic
absolute risk aversion, and employing the basic skills of mathematical modelling. The solution
to the model was sought by formulating a continuous-time utility portfolio model satisfying some
uncertainty criteria where the investment is continuous, the investor does not possess enough
power to determine price and the investor can borrow money for a given period at a particular
interest rate. The model was solved using analytical method and numerical method and optimal
values of some input factors are derived.