2019/07/31 by Álvaro Cartea, Cartea, Alvaro, Ryan Donnelly +3
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Risk and Portfolio Optimization #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.1908.00054
openalex publication_date 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A risk-averse agent hedges her exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the non-tradable risk factor ψ(UT) is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when ψ(UT) is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.