Abstract

We consider an optimal investment problem for an investor facing constant and proportional transaction costs and study the limit as the constant cost tends to zero. Combining the stochastic Perron's method with stability arguments for viscosity solutions, we show that the value function converges to the value function of the problem with purely proportional costs. Moreover, using a Komlos-type argument, we show that forward-convex combinations of the optimal strategies in the problem with constant costs converge to an optimal strategy without a constant cost.

Keywords

  1. optimal investment
  2. transaction costs
  3. stochastic Perron
  4. viscosity solutions

MSC codes

  1. 91G80
  2. 93E20
  3. 35D40

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 2712 - 2736
ISSN (online): 1095-7138

History

Submitted: 29 November 2021
Accepted: 15 June 2022
Published online: 13 September 2022

Keywords

  1. optimal investment
  2. transaction costs
  3. stochastic Perron
  4. viscosity solutions

MSC codes

  1. 91G80
  2. 93E20
  3. 35D40

Authors

Affiliations

Funding Information

Susan M. Smith
National Science Foundation https://doi.org/10.13039/100000001 : DMS-2106556

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