The liquidity discount (Q2774427)

Even in the most liquid financial markets the orders to purchase or sell assets are not executed immediately. The quantity of the securities traded has an effect on their price that is called the liquidity discount. NEWLINENEWLINENEWLINEThe author analyzes the problem that faces an investor, holding a certain number of shares of a stock, who wants to maximize the expected utility of consumption at the initial time. It is assumed that each order to sell takes a positive time to be executed producing an instantaneous jump in the stock price process which, in between trades, follows a geometric Brownian motion. Under appropriate conditions on the utility function, the order-clearing time and the price jumps, the corresponding impulse control problem has an optimal policy that involves the transaction of all holdings at the terminal date. When the utility function belongs to a particular class, an analytical expression for the liquidity discount is derived.