Finite Horizon Optimal Investment and Consumption with Transaction Costs

Dai, Min; Jiang, Lishang; Li, Peifan; Yi, Fahuai

doi:10.2139/ssrn.1518174

Cited by 19 publications

(7 citation statements)

References 24 publications

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“…Similar results were obtained in the study of finite horizon portfolio selection with transaction costs (cf. [4,6,7,19]). The intuition is that if the investor does not have a long enough time horizon to recover at least the transaction costs, then she/he should not initiate a long position (bear in mind that the terminal position must be flat).…”

Section: Remarkmentioning

confidence: 99%

Trend Following Trading under a Regime Switching Model

Dai¹,

Zhang²,

Zhu³

2010

SIAM J. Finan. Math.

112

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Abstract. This paper is concerned with the optimality of a trend following trading rule. The idea is to catch a bull market at its early stage, ride the trend, and liquidate the position at the first evidence of the subsequent bear market. We characterize the bull and bear phases of the markets mathematically using the conditional probabilities of the bull market given the up to date stock prices. The optimal buying and selling times are given in terms of a sequence of stopping times determined by two threshold curves. Numerical experiments are conducted to validate the theoretical results and demonstrate how they perform in a marketplace. 1. Introduction. Trading in organized exchanges has increasingly become an integrated part of our life. Big moves of market indices of major stock exchanges all over the world are often the headlines of news media. By and large, active market participants can be classified into two groups according to their trading strategies: those who trade contra-trend and those who follow the trend. On the other hand, there are also passive market participants who simply buy and hold for a long period of time (often indirectly through mutual funds). Within each group of strategies there are numerous technical methods. Much effort has been devoted to theoretical analysis of these strategies.Using optimal stopping time to study optimal exit strategy for stock holdings has become the standard textbook method. For example, Øksendal [24, Examples 10.2.2 and 10.4.2] considered optimal exit strategy for stocks whose price dynamics were modeled by a geometric Brownian motion. To maximize an expected return discounted by the risk-free interest rate, the analysis in [24] showed that if the drift of the geometric Brownian motion was not high enough in comparison to the discount of interest rate, then one should sell at a given threshold. Although the model of a single geometric Brownian motion with a constant drift was somewhat too simplistic, this result well illustrated the flaw of the so-called buy and hold strategy, which worked only in limited situations. Stock selling rules under more realistic models have gained increasing attention. For example, Zhang [31] considered a selling rule determined by two

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Section: Remarkmentioning

confidence: 99%

Trend Following Trading under a Regime Switching Model

Dai¹,

Zhang²,

Zhu³

2010

SIAM J. Finan. Math.

112

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“…For example, it can be extended to including the consumption term (see Dai et al [5]). Also, the approach can be used to deal with the infinite-horizon problem discussed by Davis and Norman [6] and Shreve and Soner [21].…”

Section: Resultsmentioning

confidence: 99%

Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem

Dai¹,

Yi²

2009

Journal of Differential Equations

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124

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This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. From the angle of stochastic control, it is a singular control problem, whose value function is governed by a time-dependent HJB equation with gradient constraints. We reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well-developed theory of obstacle problem to attack the problem. The C 2,1 regularity of the value function is proven and the behaviors of the free boundaries are completely characterized.

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“…Constraints in the optimization problem are considered in Cuoco (1997), Elie and Touzi (2008) and Grandits (2015). Moreover, Akian et al (1996), Altarovici et al (2017 and Dai et al (2009) analyze the portfolio problem under transaction costs. The application of HARA utility functions in a life-cycle context can be found in Huang and Milevsky (2008), Ye (2008), Chang and Rong (2014), and Wang et al (2017).…”

Section: Introductionmentioning

confidence: 99%