2019/02/24 by Le Yang, Yang, Le, Yueyang Zheng +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60G15 #60H10 #91G80 #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:60G15 #msc:60H10 #msc:91G80 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1902.08928
25 pages, 4 figures
openalex publication_date 2019/02/24 · openalex created_date 2019/03/02 · arxiv created 2019/07/11 · arxiv updated 2019/07/12 · openalex updated_date 2026/07/28
This paper is concerned with an optimal investment problem under correlated noises in the financial market, and the expected utility functional is hyperbolic absolute risk aversion (HARA) with the exponent γ≠0. The problem can be reformulated as a risk-sensitive stochastic control problem. A new stochastic maximum principle is obtained first, where the adjoint equations and maximum condition heavily depend on the risk-sensitive parameter and the correlation coefficient. The optimal investment strategy is obtained explicitly in a state feedback form via the solution to a certain Riccati equation, under the risk-seeking case. Numerical simulation and figures are given to illustrate the sensitivity for the optimal investment strategy, with respect to the risk-sensitive parameter and the correlation coefficient.