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Nonlinear price impact and portfolio choice
Author(s) -
Guasoni Paolo,
Weber Marko Hans
Publication year - 2020
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12234
Subject(s) - economics , portfolio , asset (computer security) , econometrics , market impact , constant (computer programming) , nonlinear system , geometric brownian motion , capital asset pricing model , order (exchange) , financial economics , market microstructure , computer science , physics , computer security , economy , finance , diffusion process , quantum mechanics , programming language , service (business)
Abstract In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long‐term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square‐root impact law and, as extreme cases, linear impact and proportional transaction costs.