Smooth investment

Kenneth Bruhn (), Ninna Reitzel Jensen () and Mogens Steffensen ()
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Kenneth Bruhn: University of Copenhagen
Ninna Reitzel Jensen: University of Copenhagen
Mogens Steffensen: University of Copenhagen

Annals of Finance, 2016, vol. 12, issue 3, No 3, 335-361

Abstract: Abstract In the classical portfolio optimization problem considered by Merton, the resulting constant proportion investment plan requires a diffusive trading strategy. This means that, within any arbitrarily small time interval, the investor must impractically both buy and sell stocks. We study the problems of a mean-square and a power utility investor for whom the trading strategy is constrained to be smooth, i.e. nondiffusive. This means that over sufficiently small time intervals, the investor is either a seller or a buyer of stocks. The mathematical framework is built around quadratic objectives such that trading activity is punished quadratically. Mean-square utility is quadratic, and power utility is covered by quadratic punishment of distance to Merton’s power utility portfolio. We present semi-explicit solutions and, in a series of numerical illustrations, show the impact of trading constraints on the portfolio decision over the investment horizon.

Keywords: Smooth investment; Diffusive trading; Trading costs; Power utility; Mean-square utility (search for similar items in EconPapers)
JEL-codes: C61 D11 D81 G11 G12 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10436-016-0283-7

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