{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T08:39:50Z","timestamp":1792658390126,"version":"4.5.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We study the optimal sequential purchase and sale of a single asset in a partially observable market. The asset price follows a geometric Brownian motion whose drift switches between a bull and a bear value according to an unobservable two-state Markov chain, and every transaction incurs a proportional cost. Replacing the hidden regime by the Wonham filter, we characterize the value functions by quasi-variational inequalities, which reduce to a linear second-order ordinary differential equation on (0, 1) with irregular singular points at both ends. We show that the value functions are finite when the discount rate exceeds the growth rate of the expected price and infinite when it is smaller, identify the value functions with the solutions that are bounded at the two entrance boundaries, and show that the optimal buy and sell thresholds solve a two-point problem that does not depend on the choice of basis of solutions. A comparison principle shows that the thresholds exist if and only if the transaction cost is below an explicit critical value, that they are unique, and that the no-trading region widens with the cost; for small costs its width is of order K 1\/3 , with an explicit constant. A verification theorem establishes that the resulting threshold (trendfollowing) rule is optimal, and an explicit full-information benchmark measures the cost of not observing the regime. Monte Carlo simulations support the computed value functions and indicate robustness to moderate parameter misspecification. In historical tests using parameters estimated from past data, the strategy does not outperform buy-and-hold in terminal wealth over the full samples. For the S&amp;amp;P 500, it substantially reduces volatility and maximum drawdown while achieving a comparable Sharpe ratio. For Apple, it performs relatively well during 1991-2008 but underperforms buy-and-hold and the moving-average benchmark during 2009-2026.<\/jats:p>","DOI":"10.2139\/ssrn.7645938","type":"posted-content","created":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T08:00:37Z","timestamp":1792656037000},"source":"Crossref","is-referenced-by-count":0,"title":["Optimal Trading in a Partially Observable Market"],"prefix":"10.2139","author":[{"given":"Duy","family":"Nguyen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Q.","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T08:00:37Z","timestamp":1792656037000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7645938"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7645938","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}