Utility Maximization in a Multidimensional Market with Small Nonlinear Price Impact

We study a portfolio choice problem in a multi-dimensional market with frictions. An investor with constant relative risk aversion invests in a market composed of a riskless asset and a multi-dimensional risky asset. Trading... [ view full abstract ]

We study a portfolio choice problem in a multi-dimensional market with frictions. An investor with constant relative risk aversion invests in a market composed of a riskless asset and a multi-dimensional risky asset. Trading is hindered by sublinear price impacts that affect the asset traded but possibly also the other risky assets. In the limit for small price impact, we determine the asymptotic expansion of the value function and provide an asymptotically optimal family of trading strategies.
This a joint work with Erhan Bayraktar and Ibrahim Ekren.