2019/05/30 by Erhan Bayraktar, Xin Zhang, Bayraktar, Erhan +1
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1905.12811
openalex publication_date 2019/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (Z,κ) be a Walsh Brownian motion with spinning measure κ. Suppose μ is a probability measure on ℝn. We characterize all the κ such that μ is a stopping distribution of (Z,κ). If we further restrict the solution to be integrable, we show that there would be only one choice of κ. We also generalize Vallois' embedding, and prove that it minimizes the expectation 𝔼[Ψ(LZτ)] among all the admissible solutions τ, where Ψ is a strictly convex function and (LtZ)t ≥ 0 is the local time of the Walsh Brownian motion at the origin.