Optimal Liquidation of an Asset under Drift Uncertainty

We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability distribution to characterise the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first passage time of the posterior mean below a monotone boundary, which can be characterised as the unique solution to a non-linear integral equation. We also study monotonicity properties with respect to the prior distribution and the asset volatility.

[1]  Bing Lu,et al.  Optimal Selling of an Asset with Jumps Under Incomplete Information , 2013 .

[2]  Vicky Henderson,et al.  An explicit solution for an optimal stopping/optimal control problem which models an asset sale. , 2008 .

[3]  Michael U. Dothan,et al.  Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy , 1986 .

[4]  Michael Monoyios.  Optimal investment and hedging under partial and inside information , 2009 .

[5]  S. Shreve,et al.  Methods of Mathematical Finance , 2010 .

[6]  Alexandre Ziegler,et al.  Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance , 2003 .

[7]  G. Peskir.  A Change-of-Variable Formula with Local Time on Curves , 2005 .

[8]  Jacques du Toit,et al.  Selling a Stock at the Ultimate Maximum , 2009, 0908.1014.

[9]  S. Jacka.  Optimal Stopping and the American Put , 1991 .

[10]  Christoph Reisinger,et al.  Stochastic Evolution Equations in Portfolio Credit Modelling , 2011, SIAM J. Financial Math..

[11]  Xiongzhi Chen.  Brownian Motion and Stochastic Calculus , 2008 .

[12]  Erik Ekström,et al.  Optimal Selling of an Asset under Incomplete Information , 2011 .

[13]  Vicky Henderson,et al.  OPTIMAL TIMING FOR AN INDIVISIBLE ASSET SALE , 2008 .

[14]  Stéphane Villeneuve,et al.  Investment Timing Under Incomplete Information , 2003, Math. Oper. Res..

[15]  Erik Ekström,et al.  Convexity theory for the term structure equation , 2008, Finance Stochastics.

[16]  Peter Lakner,et al.  Utility maximization with partial information , 1995 .

[17]  J. M. Corcuera,et al.  On the Optimal Investment , 2016 .

[18]  P. Protter.  Stochastic integration and differential equations , 1990 .

[19]  Michael Monoyios,et al.  Optimal exercise of an executive stock option by an insider , 2011 .

[20]  Jessica Schulze.  Incomplete Information And Heterogeneous Beliefs In Continuous Time Finance , 2016 .

[21]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[22]  P. Moerbeke.  On optimal stopping and free boundary problems , 1973, Advances in Applied Probability.

[23]  Tomas Björk,et al.  Optimal investment under partial information , 2010, Math. Methods Oper. Res..

[24]  Kerry Back,et al.  Incomplete and Asymmetric Information in Asset Pricing Theory , 2004 .

[25]  P. Lakner.  Optimal trading strategy for an investor: the case of partial information , 1998 .

[26]  H. R. Lerche,et al.  A New Look at Optimal Stopping Problems related to Mathematical Finance , 1997 .

[27]  D. Crisan,et al.  Fundamentals of Stochastic Filtering , 2008 .

[28]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[29]  P. Gapeev.  Pricing of Perpetual American Options in a Model with Partial Information , 2010 .

[30]  G. Peskir.  ON THE AMERICAN OPTION PROBLEM , 2005 .