Optimal Investment for Retail Investors with Floored and Capped Costs

33 Pages Posted: 3 Sep 2019

See all articles by Christoph Belak

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Lukas Mich

University of Trier

Frank Thomas Seifried

University of Trier

Date Written: September 3, 2019

Abstract

We study optimal portfolio decisions for a retail investor that faces proportional costs which are floored and capped at some minimal and maximal cost levels, respectively, in a classical Black-Scholes market. We provide a construction of optimal trading strategies and characterize the value function as the unique viscosity solution of the associated quasi-variational inequalities. Moreover, we numerically investigate the optimal trading regions and find a distinct structure: The no-trading region is vVv-shaped, and all optimal trades for small (large) levels of wealth incur the floored (capped) cost; proportional cost trades occur only in a narrow intermediate wealth regime.

Keywords: Portfolio Optimization, Transaction Costs, Retail Investor

JEL Classification: G11, C61

Suggested Citation

Belak, Christoph and Mich, Lukas and Seifried, Frank Thomas, Optimal Investment for Retail Investors with Floored and Capped Costs (September 3, 2019). Available at SSRN: https://ssrn.com/abstract=3447346 or http://dx.doi.org/10.2139/ssrn.3447346

Christoph Belak (Contact Author)

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Lukas Mich

University of Trier ( email )

15, Universitaetsring
Trier, 54286
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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