Growth Optimal Portfolio Selection Under Proportional Transaction Costs with Obligatory Diversification

A continuous time long run growth optimal or optimal logarithmic utility portfolio with proportional transaction costs consisting of a fixed proportional cost and a cost proportional to the volume of transaction is considered. The asset prices are modeled as exponent of diffusion with jumps whose parameters depend on a finite state Markov process of economic factors. An obligatory portfolio diversification is introduced, accordingly to which it is required to invest at least a fixed small portion of our wealth in each asset.     

Efficient portfolios in financial markets with proportional transaction costs

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general multi-currency financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. We provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig (Rev Financ Stud 1:67–88, 1988) and Jouini and Kallal (J Econ Theory 66: 178–197, 1995). We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system that prices it. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading, and give a dual representation of it as the largest proportion of the market price necessary for all agents to reach the same expected utility level.     

Asset allocation with distorted beliefs and transaction costs

In this paper we study the problem of the optimal portfolio selection with transaction costs for a decision-maker who is faced with Knightian uncertainty. The decision-maker’s portfolio consists of one risky and one risk-free asset, and we assume that the transaction costs are proportional to the traded volume of the risky asset. The attitude to uncertainty is modeled by the Choquet expected utility. We derive optimal strategies and bounds of the no-transaction region for both optimistic and pessimistic decision-makers. The no-transaction region of a pessimistic investor is narrower and its bounds lie closer to the origin than that of an optimistic trader. Moreover, under the Choquet expected utility the structure of the no-transaction region is not necessarily a closed interval as it is under the standard expected utility model.     

Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs

Abstract

Portfolio theory covers different approaches to the construction of a portfolio offering maximum expected returns for a given level of risk tolerance where the goal is to find the optimal investment rule. Each investor has a certain utility for money which is reflected by the choice of a utility function. In this article, a risk averse power utility function is studied in discrete time for a large class of underlying probability distribution of the returns of the asset prices. Each investor chooses, at the beginning of an investment period, the feasible portfolio allocation which maximizes the expected value of the utility function for terminal wealth. Effects of both large and small proportional transaction costs on the choice of an optimal portfolio are taken into account. The transaction regions are approximated by using asymptotic methods when the proportional transaction costs are small and by using expansions about critical points for large transaction costs.     

考虑相对业绩的最优投资选择博弈问题研究

研究了具有相互作用的两个竞争机构投资者之间的离散时间最优投资选择博弈问题,每个机构投资者都考虑其竞争对手的相对业绩.机构投资者可以投资于相同的无风险资产和不同的具有相关关系的风险股票,以反映投资的资产专门化.机构投资者选择投资组合策略使得期望终端绝对财富和相对财富的效用最大.首先,定义了Nash均衡投资组合选择策略.然后,在机构投资者具有指数效用函数的假设下,得到了Nash均衡投资组合选择策略和值函数的显示表达式,分析了机构投资者之间的竞争对Nash均衡投资组合选择策略的影响.最后,通过数值计算给出了各种情况下Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系.结果表明:机构投资者之间的竞争会影响其对风险的承担,投资机会集对机构投资者的Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系会产生很大的影响.     

Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis

In this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.     

Multi‐asset portfolio optimization with transaction cost

The inclusion of transaction costs in the optimal portfolio selection and consumption rule problem is accomplished via the use of perturbation analyses. The portfolio under consideration consists of more than one risky asset, which makes numerical methods impractical. The objective is to establish both the transaction and the no‐transaction regions that characterize the optimal investment strategy. The optimal transaction boundaries for two and three risky assets portfolios are solved explicitly. A procedure for solving the N risky assets portfolio is described. The formulation used also reduces the restriction on the functional form of the utility preference.     

Portfolio optimization with linear and fixed transaction costs

We consider the problem of portfolio selection, with transaction costs and constraints on exposure to risk. Linear transaction costs, bounds on the variance of the return, and bounds on different shortfall probabilities are efficiently handled by convex optimization methods. For such problems, the globally optimal portfolio can be computed very rapidly. Portfolio optimization problems with transaction costs that include a fixed fee, or discount breakpoints, cannot be directly solved by convex optimization. We describe a relaxation method which yields an easily computable upper bound via convex optimization. We also describe a heuristic method for finding a suboptimal portfolio, which is based on solving a small number of convex optimization problems (and hence can be done efficiently). Thus, we produce a suboptimal solution, and also an upper bound on the optimal solution. Numerical experiments suggest that for practical problems the gap between the two is small, even for large problems involving hundreds of assets. The same approach can be used for related problems, such as that of tracking an index with a portfolio consisting of a small number of assets.     

On an investment-consumption model with transaction costs: an asymptotic analysis

In this paper we examine the Akian, Menaldi and Sulem (1996) model for the optimal management of a portfolio, when there are transaction costs which are equal to a fixed percentage of the amount transacted. We analyse this model in the realistic limit of small transaction costs. Although the full problem is a free boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.     

Merton problem in a discrete market with frictions

We study the classical optimal investment and consumption problem of Merton in a discrete time model with frictions. Market friction causes the investor to lose wealth due to trading. This loss is modeled through a nonlinear penalty function of the portfolio adjustment. The classical transaction cost and the liquidity models are included in this abstract formulation. The investor maximizes her utility derived from consumption and the final portfolio position. The utility is modeled as the expected value of the discounted sum of the utilities from each step. At the final time, the stock positions are liquidated and a utility is obtained from the resulting cash value. The controls are the investment and the consumption decisions at each time. The utility function is maximized over all controls that keep the after liquidation value of the portfolio non-negative. A dynamic programming principle is proved and the value function is characterized as its unique solution with appropriate initial data. Optimal investment and consumption strategies are constructed as well.     

Intertemporal portfolio optimization with small transaction costs and stochastic variance

The solution to the intertemporal optimal portfolio selection and consumption rule with small transaction costs is derived via the use of perturbation analysis for the two assets portfolio, one risky and one riskfree. This methodology allows us to apply a broader specification for the function of utility. The additional feature of stochastic variance is also included.     

A unified approach to portfolio optimization with linear transaction costs

In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.     

Optimal rebalancing of portfolios with transaction costs

Rebalancing of portfolios with a concave utility function is considered. It is proved that transaction costs imply that there is a no-trade region where it is optimal not to trade. For proportional transaction costs, it is optimal to rebalance to the boundary when outside the no-trade region. With flat transaction costs, the rebalance from outside the no-trade region should be to an internal state in the no-trade region but never a full rebalance. The standard optimal portfolio theory is extended to an arbitrary number of equally treated assets, general utility function and more general stochastic processes. Examples are discussed.     

VaR optimal portfolio with transaction costs

We consider the problem of portfolio optimization under VaR risk measure taking into account transaction costs. Fixed costs as well as impact costs as a nonlinear function of trading activity are incorporated in the optimal portfolio model. Thus the obtained model is a nonlinear optimization problem with nonsmooth objective function. The model is solved by an iterative method based on a smoothing VaR technique. We prove the convergence of the considered iterative procedure and demonstrate the nontrivial influence of transaction costs on the optimal portfolio weights.     

Selecting Portfolios with Fixed Costs and Minimum Transaction Lots

The original Markowitz model of portfolio selection has received a widespread theoretical acceptance and it has been the basis for various portfolio selection techniques. Nevertheless, this normative model has found relatively little application in practice when some additional features, such as fixed costs and minimum transaction lots, are relevant in the portfolio selection problem. In this paper different mixed-integer linear programming models dealing with fixed costs and possibly minimum lots are introduced. Due to the high computational complexity of the models, heuristic procedures, based on the construction and optimal solution of mixed integer subproblems, are proposed. Computational results obtained using data from the Milan Stock Exchange show how the proposed heuristics yield very good solutions in a short computational time and make possible some interesting financial conclusions on the impact of fixed costs and minimum lots on portfolio composition.     

Perturbation solution of optimal portfolio theory with transaction costs for any utility function

The solution to the optimal portfolio selection and consumptionrule with small transaction costs is derived via the use ofperturbation analysis for the case when one risky and one risklessasset are available for investment. This methodology allowsus to apply a broader specification for the utility function.     

共同资金投资组合的有效边界与最优策略

本文利用均值方差模型,分析了非线性交易成本下的共同资金投资的有效边界和在一般的效用函数下讨论了最优投资组合和最大效用,其中只考虑风险资产的总投资比例对交易成本的影响.     

Optimal and robust contracts for a risk-constrained principal

The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem. The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal’s optimal choice.     

Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model

This paper is concerned with an infinite-horizon problem of optimal investment and consumption with proportional transaction costs in continuous-time regime-switching models. An investor distributes his/her wealth between a stock and a bond and consumes at a non-negative rate from the bond account. The market parameters (the interest rate, the appreciation rate, and the volatility rate of the stock) are assumed to depend on a continuous-time Markov chain with a finite number of states (also known as regimes). The objective of the optimization problem is to maximize the expected discounted total utility of consumption. We first show that for a class of hyperbolic absolute risk aversion utility functions, the value function is a viscosity solution of the Hamilton–Jacobi–Bellman equation associated with the optimization problem. We then treat a power utility function and generalize the existing results to the regime-switching case.     

Impulsive Control of Portfolios

In this paper a general model of a market with asset prices and economical factors of Markovian structure is considered. The problem is to find optimal portfolio strategies maximizing a discounted infinite horizon reward functional consisting of an integral term measuring the quality of the portfolio at each moment and a discrete term measuring the reward from consumption. There are general transaction costs which, in particular, cover fixed plus proportional costs. It is shown, under general conditions, that there exists an optimal impulse strategy and the value function is a solution to the Bellman equation which corresponds to suitable quasi-variational inequalities.