Transactions costs and portfolio choice in a discrete-continuous-time setting

Liquidity shocks and equilibrium liquidity premia

“…Because of the law of large numbers, agents exit at a rate of l per unit of time, leaving the economy with a constant mass of agents. 6 See, for example, [12,[14][15][16]19,27,31,32]. 7 Without loss of generality, our set of agents is the unit interval.…”

“…Consider an alternate policy that deviates from the candidate policy by investing one unit in the illiquid consol at time t and reinvesting all of its dividends in the liquid consol. 15 By adopting such a deviation, in the event of a liquidity shock at some time s4t; the agent's consumption changes by 16 1…”

“…Proposition 1. Suppose W 0 40 and y ¼ 0: The optimal policy ða; AÞ is given by 15 We do not consider a local deviation of policy here because it is never optimal to sell the illiquid consol before a liquidity shock. 16 One unit invested at t according to the candidate policy grows to e rðsÀtÞ at s: One unit invested at t according to the alternate policy generates 1 1þe shares of the illiquid consol (which pays off 1Àe 1þe at s), plus the dividends rolled over into the liquid consol between time t and s; 1 1þe R s t Re rðsÀuÞ du: The difference between the two approaches gives (9).…”

Portfolio Selection with Transaction Costs

“…[2], [5], [8], [9], [11] . Of the recent contributions, [2] and [11] include transaction costs. [2] shows how the presence of a minimum cost per transaction gives rise to discrete optimal trading in random intervals, while [11] solves a two-asset capital growth problem with proportional transaction costs and proves that the optimal strategy is a control limit policy which confines the investor's portfolio to a certain wedgeshaped region by minimal (continuous) trading at the barriers .…”

Asset allocation and liquidity breakdowns: what if your broker does not answer the phone?

“…A second strand of literature introduces transaction costs into the model implying that it is not optimal for investors to trade continuously. Papers in this area include Duffie and Sun (1990), Davis and Norman (1990), and Korn (1998), among others. Besides, Longstaff (2001) looks at the portfolio problem of an investor who can only implement portfolio strategies with finite variation and thus faces liquidity constraints.…”