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Open AccessFeature PaperArticle

Optimal Timing to Trade along a Randomized Brownian Bridge

by Tim Leung 1,*, Jiao Li 2 and Xin Li 3
1
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
2
APAM Department, Columbia University, New York, NY 10027, USA
3
Bank of America Merrill Lynch, One Bryant Park, New York, NY 10036, USA
*
Author to whom correspondence should be addressed.
Int. J. Financial Stud. 2018, 6(3), 75; https://doi.org/10.3390/ijfs6030075
Received: 31 December 2017 / Revised: 27 July 2018 / Accepted: 3 August 2018 / Published: 30 August 2018
(This article belongs to the Special Issue Finance, Financial Risk Management and their Applications)
This paper studies an optimal trading problem that incorporates the trader’s market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by an exponential randomized Brownian bridge (rBb) and consider various prior distributions for the random endpoint. We solve for the optimal strategies to sell a stock, call, or put, and analyze the associated delayed liquidation premia. We solve for the optimal trading strategies numerically and compare them across different prior beliefs. Among our results, we find that disconnected continuation/exercise regions arise when the trader prescribe a two-point discrete distribution and double exponential distribution. View Full-Text
Keywords: speculative trading; Brownian bridge; optimal stopping; variational inequality speculative trading; Brownian bridge; optimal stopping; variational inequality
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Leung, T.; Li, J.; Li, X. Optimal Timing to Trade along a Randomized Brownian Bridge. Int. J. Financial Stud. 2018, 6, 75.

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