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• W797785281 abstract "The problem of maximizing the expected utility from terminal wealth is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market containing a bond and a finite number of stocks, whose prices are driven by a multidimensional Brownian motion process W. The coefficients of the bond and stock processes are adapted to the filtration (history) of W, and incompleteness arises when the number of stocks is strictly smaller than the dimension of W. It is shown that there is a way to complete the market by introducing additional, fictitious stocks, so that the optimal portfolio for the thus completed market coincides with the optimal portfolio for the original incomplete market. The notion of a least favorable completion is introduced and is shown to be closely related to the existence question for an optimal portfolio in the incomplete market. This notion is expounded upon using martingale techniques; several equivalent characterizations are provided for it, examples are studied in detail, and a fairly general existence result for an optimal portfolio is established based on convex duality theory." @default.
• W797785281 created "2016-06-24" @default.
• W797785281 creator A5060473555 @default.
• W797785281 date "1989-01-01" @default.
• W797785281 modified "2023-09-27" @default.
• W797785281 title "Martingale and duality methods for utuility [i.e., utility] maximization in an incomplete market" @default.
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