2017/05/23 by Oleksii Mostovyi, Mostovyi, Oleksii, Mihai Ŝırbu +2 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #91G10 #93E20 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #math.PR #msc:91G10 #msc:93E20 #q-fin.PM
paper · pdf · doi:10.48550/arxiv.1705.08291
preliminary version
arxiv created 2017/05/23 · openalex publication_date 2017/05/23 · arxiv updated 2017/05/24 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
We study the sensitivity of the expected utility maximization problem in a continuous semi-martingale market with respect to small changes in the market price of risk. Assuming that the preferences of a rational economic agent are modeled with a general utility function, we obtain a second-order expansion of the value function, a first-order approximation of the terminal wealth, and construct trading strategies that match the indirect utility function up to the second order. If a risk-tolerance wealth process exists, using it as a numéraire and under an appropriate change of measure, we reduce the approximation problem to a Kunita-Watanabe decomposition.