Optimal investment and consumption under a continuous-time cointegration model with exponential utility

Ma, Guiyuan; Zhu, Song‐Ping

doi:10.1080/14697688.2019.1570317

Cited by 27 publications

(9 citation statements)

References 32 publications

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“…We briefly mention more recent studies related to continuous-time portfolio optimization. (i) Regarding objective functions, we list some studies: the risk-sensitive criterion [HS17]; the conditional value-at-risk (or expected shortfall) [MY17]; the power utility [ET08]; and the exponential utility [MZ19]. (ii) The mean-variance portfolio optimization has been also investigated in the continuous-time setting.…”

Section: Introductionmentioning

confidence: 99%

Continuous-time Portfolio Optimization for Absolute Return Funds

Ieda¹

2021

Preprint

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This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a performance criterion based on the lower mean square error between the investor's wealth and a predetermined target wealth level. Since the target level is defined by a deterministic function independent of market indices, it corresponds to the criterion of absolute return funds. The model is formulated using the stochastic control framework with explicit boundary conditions. The corresponding Hamilton-Jacobi-Bellman equation is solved numerically using the kernel-based collocation method. However, a straightforward implementation does not offer a stable and acceptable investment strategy; thus, some techniques to address this shortcoming are proposed. By applying the proposed methodology, two numerical results are obtained: one uses artificial data, and the other uses empirical data from Japanese organizations. There are two implications from the first result: how to stabilize the numerical solution, and a technique to circumvent the plummeting achievement rate close to the terminal time. The second result implies that leverage is inevitable to achieve the target level in the setting discussed in this paper.

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Section: Introductionmentioning

confidence: 99%

Continuous-time Portfolio Optimization for Absolute Return Funds

Ieda¹

2021

Preprint

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“…Ever since the development of the Black-Scholes derivative pricing model and the Merton portfolio selection model, a large amount of research interest has been led into this area, and various analytical as well as numerical approaches together with their applications in finance practice have been discussed [16,23,24,27,28,29,30,31,32,34,35,36]. In fact, optimal portfolio selection problem is essentially to achieve a balance between uncertain returns and risks, for which the mean-variance methodology has become one of the most important tools, ever since Markowitz's pioneering work on a static investment model [25].…”

Section: Introductionmentioning

confidence: 99%

Continuous time mean-variance-utility portfolio problem and its equilibrium strategy

Yang

Zhu

2020

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In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean variance criterion controlling the final risk of the portfolio. The multiple-objective optimization problem is firstly transformed into a single-objective one by introducing the concept of overall "happiness" of an investor defined as the aggregation of the terminal wealth under the mean-variance criterion and the expected accumulated utility, and then solved under a game theoretic framework. We have managed to maintain analytical tractability; the closed-form solutions found for a set of special utility functions enable us to discuss some interesting optimal investment strategies that have not been revealed before in literature.

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“…Since Markowitz's pioneering work on a static portfolio selection model [19], mean-variance problem has become one of the most important tools in finance to achieve a balance between uncertain returns and risks. Under mean-variance framework, there are several models have been proposed and developed to address investment problems, which have attracted a lot of attention from both academic researchers and market practitioners [18,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Mean-variance-utility portfolio selection with time and state dependent risk aversion

Yang,

He,

Zhu

2020

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Under mean-variance-utility framework, we propose a new portfolio selection model, which allows wealth and time both have influences on risk aversion in the process of investment. We solved the model under a game theoretic framework and analytically derived the equilibrium investment (consumption) policy. The results conform with the facts that optimal investment strategy heavily depends on the investor's wealth and future income-consumption balance as well as the continuous optimally consumption process is highly dependent on the consumption preference of the investor.

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Optimal investment and consumption under a continuous-time cointegration model with exponential utility

Cited by 27 publications

References 32 publications

Continuous-time Portfolio Optimization for Absolute Return Funds

Continuous-time Portfolio Optimization for Absolute Return Funds

Continuous time mean-variance-utility portfolio problem and its equilibrium strategy

Mean-variance-utility portfolio selection with time and state dependent risk aversion

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