2022/08/30 by Marcos Escobar‐Anel, Escobar-Anel, Marcos, Yevhen Havrylenko +3
Decision Sciences · Economics, Econometrics and Finance · #49L20 (Secondary) #90C39 (Secondary) #91G10 (Primary) #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Market Dynamics and Volatility #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2208.14152
openalex publication_date 2022/08/30 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic programming approach. We demonstrate that the value function in the constrained problem can be represented as the expected modified utility function of a vega-neutral financial derivative on the optimal terminal wealth in the unconstrained utility-maximization problem. Via the same financial derivative, the optimal wealth and the optimal investment strategy in the constrained problem are linked to the optimal wealth and the optimal investment strategy in the unconstrained problem. In numerical studies, we substantiate the impact of risk aversion levels and investment horizons on the optimal investment strategy. We observe a 20% relative difference between the constrained and unconstrained allocations for average parameters in a low-risk-aversion short-horizon setting.