2013/06/03 by Chen Xiaoshan, Xiaoshan, Chen, Song Qingshuo +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Geometric Analysis and Curvature Flows #Insurance, Mortality, Demography, Risk Management #Nonlinear Partial Differential Equations #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications #math.PR #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1306.0345
19 pages, 4 figures
arxiv created 2013/06/03 · openalex publication_date 2013/06/03 · arxiv updated 2013/06/04 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
In this paper we study a general framework of American put option with stochastic volatility whose value function is associated with a 2-dimensional parabolic variational inequality with degenerate boundaries. We apply PDE methods to analyze the existences of the strong solution and the properties of the 2-dimensional manifold for the free boundary. Thanks to the regularity result on the solution of the underlying PDE, we can also provide the uniqueness of the solution by the argument of the verification theorem together with the generalized Ito's formula even though the solution may not be second order differentiable in the space variable across the free boundary.