2019/09/06 by Bernardo D’Auria, Bernardo D'Auria, D'Auria, Bernardo +2
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #60G40 #60H30 #91B26 #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #Supply Chain and Inventory Management #math.OC #math.PR #msc:60G40 #msc:60H30 #msc:91B26
paper · pdf · doi:10.48550/arxiv.1909.02916
9 pages, 2 figures
arxiv created 2019/09/06 · openalex publication_date 2019/09/06 · arxiv updated 2019/09/09 · openalex created_date 2019/09/12 · openalex updated_date 2026/07/28
The scope of this paper is to study the optimal stopping problems associated to a stochastic process, which may represent the gain of an investment, for which information on the final value is available a priori. This information may proceed, for example, from insider trading or from pinning at expiration of stock options. We solve and provide explicit solutions to these optimization problems. As special case, we discuss different processes whose optimal barrier has the same shape as the optimal barrier of the Brownian bridge. So doing we provide a catalogue of alternatives to the Brownian bridge which in practice could be better adapted to the data. Moreover, we investigate if, for any given (decreasing) curve, there exists a process with this curve as optimal barrier. This provides a model for the optimal liquidation time, i.e. the optimal time at which the investor should liquidate a position in order to maximize the gain.