2017/10/02 by Traian A. Pirvu, Pirvu, Traian A., Ulrich G. Haussmann +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR
paper · pdf · doi:10.48550/arxiv.1710.00939
arxiv created 2017/10/02 · openalex publication_date 2017/10/02 · arxiv updated 2017/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability measure. Traditionally, the martingale representation formulas under the risk neutral probability measure requires the market price of risk process to be bounded. However, in several financial models the boundedness assumption of the market price of risk fails. One example is a stock price model with the market price of risk following an Ornstein-Uhlenbeck process. This work extends Clark-Haussmann formula to underlying stochastic processes which fail to satisfy the standard requirements. Our result can be applied to hedging and optimal investment in stock markets with unbounded market price of risk.