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Consider a risk - averse investor with the power preferences ( where denotes the risk aversion magnitude ) and an initial fund value of W

Consider a risk-averse investor with the power preferences (where denotes the risk aversion magnitude) and an initial fund value of Wt=250,000 at date t. The investment environment offers two alternatives to the investors including: (i) a safe asset with a fixed risk-free rate RF=1+rF per invested unit between dates t and t+1; and (ii) common equity share of a private company. The equity return (RE) involves risk depending on the future company's performance. Consider that the company's dividend per share value summarises the performance and follows a Normal distribution with Dt+iN(,2) for any future date i1.
Q.1. Assume a scenario where is not pre-determined therefore the valuation depends upon the optimal value of the allocation to each asset. Assume the no-arbitrage condition and discuss the steps the investors undertakes to compute the optimal value **. The answer is expected to identify main considerations throughout the pricing procedure and provide methodological approaches used to address the considerations. Structure the answers under separate bullet points.
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