2014/02/27 by Zhongyang Sun, Xin Zhang, Sun, Zhongyang +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60H10 #93E20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #msc:60H10 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1402.6793
This paper has been withdraw by the author due to some minor error on the application of G-BSDE theory
openalex publication_date 2014/02/27 · arxiv created 2014/04/17 · arxiv updated 2014/04/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we consider the stochastic optimal control problems under model risk caused by uncertain volatilities. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brwonian motion introduced by Peng(2007). Based on the theory of stochastic differential equations on a sublinear expectation space (Ω,H,𝔼), we prove a stochastic maximum principle for controlled processes driven by G-Brownian motion. Then we obtain the maximum condition in terms of the H-function plus some convexity conditions constitute sufficient conditions for optimality. Finally, we solve a portfolio optimization problem with ambiguous volatility as an explicitly illustrated example of the main result.