We investigate a portfolio optimization problem for an agent who invests in two assets, a risk-free and a risky asset modeled by a geometric Brownian motion. The investor faces both fixed and proportional transaction costs and liquidity constraints. His objective is to maximize the expected...

This paper studies the mean-risk portfolio optimization problem with nonconvex transaction costs. We employ the conditional value-at-risk (CVaR) as a risk measure. There are a number of studies that aim at efficiently solving large-scale CVaR minimization problems. None of these studies,...

In the CRR model we introduce a transaction cost structure which covers piecewise proportional, fixed and constant costs. For a general utility function we formulate the problem of maximizing the expected utility of terminal wealth as a Markov control problem. An existence result is given and...

Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non-smooth time-dependent Hamilton–Jacobi–Bellman equation is solved by regularization and the...

This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows to obtain explicit solutions in a wide range of...