The optimal investment problem is one of the most important problems in mathematical finance. The main contribution of the present paper is an explicit formula for the optimal portfolio process. Our optimal investment problem is that of maximizing the expected value of a standard general utility function of terminal wealth in a standard complete Wiener driven financial market . In order to derive the formula for the optimal portfolio we use the recently developed functional It\^o calculus and more specifically an explicit martingale representation theorem. A main component in the formula for the optimal portfolio is a vertical derivative with respect to the driving Wiener process. The vertical derivative is an important component of functional It\^o calculus .
We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is that it relies only on an integrability condition .
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We consider a standard
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is one of the most important problems in mathematical finance. The main contribution of the present paper is an explicit formula for the optimal portfolio process. Our optimal investment problem is that of maximizing the expected value of a standard general utility function of terminal wealth in a standard complete Wiener driven financial market . In order to derive the formula for the optimal portfolio we use the recently developed functional It\^o calculus and more specifically an explicit martingale representation theorem. A main component in the
in a complete financial market driven by a Wiener process and derive an explicit
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is a vertical derivative with respect to the driving Wiener process. The vertical derivative is an important component of functional It\^o calculus
process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is that it relies only on an integrability condition