scholarly journals Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices

2016 ◽  
Author(s):  
Erhan Bayraktar ◽  
Xiang Yu
Keyword(s):  
Transaction Costs ◽  
Duality Theory ◽  
Optimal Investment ◽  
Shadow Prices

Portfolio Optimization in Incomplete Markets

2019 ◽  
pp. 426-435
Author(s):  
Tomas Björk
Keyword(s):  
Portfolio Optimization ◽  
Incomplete Markets ◽  
Duality Theory ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Finite Sample ◽  
Martingale Approach ◽  
Dual Approach ◽  
Full Theory ◽  
Optimal Investment Problem

The object of this chapter is to give an overview of the dual approach to portfolio optimization in incomplete markets. The main result of this theory is that to every optimal investment problem there is a dual problem where we minimize a dual objective function over the class of martingale measures. For the case of a finite sample space we can present the full theory, but for the general case we only outline the proof. The theory is closely connected to convex duality theory and to the martingale approach to optimal consumption/investment discussed in Chapter 27.

scholarly journals Maximization of the long-term growth rate for a portfolio with fixed and proportional transaction costs

2008 ◽  
Vol 40 (03) ◽  
pp. 673-695 ◽  
Author(s):  
Takashi Tamura
Keyword(s):  
Transaction Costs ◽  
Impulsive Control ◽  
Optimal Growth ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Proportional Transaction Costs ◽  
Average Growth ◽  
Long Run ◽  
Riskless Asset

We study the problem of maximizing the long-run average growth of total wealth for a logarithmic utility function under the existence of fixed and proportional transaction costs. The market model consists of one riskless asset and d risky assets. Impulsive control theory is applied to this problem. We derive a quasivariational inequality (QVI) of ‘ergodic’ type and obtain a weak solution for the inequality. Using this solution, we obtain an optimal investment strategy to achieve the optimal growth.

MINIMIZING THE PROBABILITY OF LIFETIME RUIN: TWO RISKLESS ASSETS WITH TRANSACTION COSTS

2019 ◽  
Vol 49 (03) ◽  
pp. 847-883
Author(s):  
Xiaoqing Liang ◽  
Virginia R. Young
Keyword(s):  
Transaction Costs ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Money Market ◽  
The Other ◽  
Proportional Transaction Costs ◽  
Optimal Investment Strategy ◽  
The Individual ◽  
Riskless Asset

AbstractWe compute the optimal investment strategy for an individual who wishes to minimize her probability of lifetime ruin. The financial market in which she invests consists of two riskless assets. One riskless asset is a money market, and she consumes from that account. The other riskless asset is a bond that earns a higher interest rate than the money market, but buying and selling bonds are subject to proportional transaction costs. We consider the following three cases. (1) The individual is allowed to borrow from both riskless assets; ruin occurs if total imputed wealth reaches zero. Under the optimal strategy, the individual does not sell short the bond. However, she might wish to borrow from the money market to fund her consumption. Thus, in the next two cases, we seek to limit borrowing from that account. (2) We assume that the individual pays a higher rate to borrow than she earns on the money market. (3) The individual is not allowed to borrow from either asset; ruin occurs if both the money market and bond accounts reach zero wealth. We prove that the borrowing rate in case (2) acts as a parameter connecting the two seemingly unrelated cases (1) and (3).

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