Let ((S, D)) be a couple of price-dividend processes not admitting arbitrage opportunities and let (u: mathbb{R}_{+}

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Let \((S, D)\) be a couple of price-dividend processes not admitting arbitrage opportunities and let \(u: \mathbb{R}_{+} \rightarrow \mathbb{R}\) be a continuous, strictly increasing and concave utility function. Prove that, for all \(x>0\), the optimal investmentconsumption problem (6.6) admits a solution in correspondence of \((S, D)\).

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