Optimal Liquidation in a Defaultable Market

Abstract

In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the firm, whose assets are available in the market for investors. Considering that selling a large number of assets has a significant impact in the price, and hence in the portfolio's value, the control problem involved to describe the optimal strategy to liquidate a large position is analyzed. Under suitable assumptions in the model, an explicit solution is given to the value function and a precise description of the optimal strategy is obtained.