2023/04/14 by Yunhong Li, Li, Yunhong, Zuo Quan Xu +3 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #35Q91 #91B28 #91G10 #FOS: Economics and business #FOS: Mathematics #Market Dynamics and Volatility #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2304.06938
openalex publication_date 2023/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution, hence an ``intractable claim''. In view of the lack of necessary information about the claim, we consider a robust formulation to maximize her utility in the worst scenario. We apply the quantile formulation to solve the problem, expressing the quantile function of the optimal terminal investment income as the solution of certain variational inequalities of ordinary differential equations and obtaining the resulting optimal trading strategy. In the case of an exponential utility, the problem reduces to a (non-robust) rank--dependent utility maximization with probability distortion whose solution is available in the literature. The results can also be used to determine the utility indifference price of the intractable claim.