Portfolio Optimization with Nondominated Priors and Unbounded Parameters

2018/07/16 by Kerem Uğurlu, Kerem Ugurlu, Ugurlu, Kerem
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #q-fin.PM

paper · pdf · doi:10.48550/arxiv.1807.05773

arxiv created 2018/07/16 · openalex publication_date 2018/07/16 · arxiv updated 2018/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertainty on the parameters of both mean and volatility. We take that the investor has logarithmic utility function, and solve the corresponding utility maximization problem explicitly. To the best of our knowledge, this is the first work on utility maximization with unbounded mean and volatility in Knightian uncertainty under nondominated priors.

Citations

• The Pricing of Options and Corporate Liabilities
• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

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