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Optimal Investment/Consumption with Liquid and Illiquid Assets

  • Event Date: November 24, 2015
  • Event End Date: November 24, 2015
  • Event Start Time: 11:45 AM
  • Event End Time: 12:45 PM
  • Event Type: Mathematical Finance and Probability Seminars
  • Extra Info: Jin Hyuk Choi, UT Autin
Date: 11/24/2015

Time: Tuesday, 11:45am-12:45pm

Speaker: Jin Hyuk Choi, UT Autin

Location: Hill 705 

Slides: ( TBA ) 




ABSTRACT 

We consider an optimal investment/consumption problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio which consists of one bond, one liquid asset (no transaction costs) and one illiquid asset (proportional transaction costs), and the asset prices follow the Black-Scholes model (with correlated Brownian motions). Using the so-called shadow price approach, we derive a free-boundary ODE with an integral constraint, and prove that there exists a smooth solution to the problem. Then we fully characterize the optimal trading and consumption strategies in terms of the solution of the free-boundary ODE. In the analysis, there is no technical assumption (except some natural ones) on the model parameters.