Mean-variance Portfolio Selection Research Articles

Mean-variance portfolio with wealth and volatility dependent risk aversion

Risk aversion rate plays a significant role in mean-variance portfolio selection. Most existing literature assumes it to be constant or wealth dependent, which is unrealistic. In this study, I contend that it is both wealth and volatility dependent because it varies across economic status: either steady or fluctuated. In addition, I decompose the risk aversion rate into a wealth prudence rate and a volatility prudence rate and investigate their mutual effect on portfolio selection under a continuous-time mean-variance framework. Using Game theoretic approach and asymptotic expansion, I derive the optimal trading rule analytically.

Stochastic intervention control of mean-field jump system with noisy observation via L-derivatives with application to finance

In this paper, we investigate stochastic optimal intervention control of mean-field nonlinear random Poisson-jump-system with related noisy process. We derive the necessary conditions of optimality for partially observed optimal intervention control problems of mean-field type. The coefficients depend on the state of the solution process as well as of its probability distribution and the control variable. The proof of our main result is obtained by applying L-derivatives in the sense of Lions. In our control model, there are two models of jumps for the state process, the inaccessible ones which come from the random Poission process and the predictable ones which come from the intervention control. Finally, we apply our result to study conditional mean-variance portfolio selection problem with interventions, where the foreign exchange interventions are intended to contain excessive fluctuations in foreign exchange rates and to stabilize them.

Tail mean-variance portfolio selection with estimation risk

Tail Mean-Variance (TMV) has emerged from the actuarial community as a criterion for risk management and portfolio selection, with a focus on extreme losses. The existing literature on portfolio optimization under the TMV criterion relies on the plug-in approach that substitutes the unknown mean vector and covariance matrix of asset returns in the optimal portfolio weights with their sample counterparts. However, the plug-in method inevitably introduces estimation risk and usually leads to poor out-of-sample portfolio performance. To address this issue, we propose a combination of the plug-in and 1/N rules and optimize its expected out-of-sample performance. Our study is based on the Mean-Variance-Standard-deviation (MVS) performance measure, which encompasses the TMV, classical Mean-Variance, and Mean-Standard-Deviation (MStD) as special cases. The MStD criterion is particularly relevant to mean-risk portfolio selection when risk is measured by quantile-based risk measures. Our proposed combined portfolio consistently outperforms both the plug-in MVS and 1/N portfolios in simulated and real-world datasets.

Naïve Markowitz policies

AbstractWe study a continuous‐time Markowitz mean–variance portfolio selection model in which a naïve agent, unaware of the underlying time‐inconsistency, continuously reoptimizes over time. We define the resulting naïve policies through the limit of discretely naïve policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naïve policies with pre‐committed optimal policies and with consistent planners' equilibrium policies in a Black–Scholes market, and find that the former achieve higher expected terminal returns than originally planned yet are mean–variance inefficient when the risk aversion level is sufficiently small, and always take strictly riskier exposure than equilibrium policies. We finally define an efficiency ratio for comparing return–risk tradeoff with the same original level of risk aversion, and show that naïve policies are always strictly less efficient than pre‐committed and equilibrium policies.

Mean-variance portfolio selection with non-linear wealth dynamics and random coefficients

This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal with the expectation constraint, an auxiliary stochastic control problem is firstly solved by two new generalized stochastic Riccati equations from which a candidate portfolio in feedback form is constructed, and the corresponding wealth process will never cross the vertex of the parabola. In order to verify the optimality of the candidate portfolio, the convex duality (requires the monotonicity of the cost function) is established to give another more direct expression of the terminal wealth level. The variance-optimal martingale measure and the link between the non-linear financial market and the classical linear market are also provided. Finally, we obtain the efficient frontier in closed form. From our results, people are more likely to invest their money in riskless asset compared with the classical linear market.

First- and Second-Order Maximum Principles for Discrete-Time Stochastic Optimal Control With Recursive Utilities

This paper deals with the discrete-time stochastic optimal control problems with recursive utilities under weakened convexity assumption. A new stochastic maximum principle is established. Moreover, by constructing two new adjoint equations and two new variational equations for the backward stochastic difference equation (BS <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta$</tex-math></inline-formula> E), we obtain the second-order necessary optimality condition of quasi-singular control. Finally, as an illustration, a discrete-time mean-variance portfolio selection mixed with a recursive utility functional optimization problem is solved.

Adaptive online mean-variance portfolio selection with transaction costs

Online portfolio selection is attracting increasing attention in both artificial intelligence and finance communities due to its efficiency and practicability in deriving optimal investment strategies in real investment activities where the market information is constantly renewed every second. The key issues in online portfolio selection include predicting the future returns of risky assets accurately given historical data and providing optimal investment strategies for investors in a short time. In the existing online portfolio selection studies, the historical return data of one risky asset is used to estimate its future return. In this paper, we incorporate the peer impact into the return prediction where the predicted return of one risky asset not only depends on its past return data but also the other risky assets in the financial market, which gives a more accurate prediction. An adaptive moving average method with peer impact (AOLPI) is proposed, in which the decaying factors can be adjusted automatically in the investment process. In addition, the adaptive mean-variance (AMV) model is firstly applied in online portfolio selection where the variance is employed to measure the investment risk and the covariance matrix can be linearly updated in the investment process. The adaptive online moving average mean-variance (AOLPIMV) algorithm is designed to provide flexible investment strategies for investors with different risk preferences. Finally, numerical experiments are presented to validate the effectiveness and advantages of AOLPIMV.

Reinforcement learning for continuous-time mean-variance portfolio selection in a regime-switching market

We propose a reinforcement learning (RL) approach to solve the continuous-time mean-variance portfolio selection problem in a regime-switching market, where the market regime is unobservable. To encourage exploration for learning, we formulate an exploratory stochastic control problem with an entropy-regularized mean-variance objective. We obtain semi-analytical representations of the optimal value function and optimal policy, which involve unknown solutions to two linear parabolic partial differential equations (PDEs). We utilize these representations to parametrize the value function and policy for learning with the unknown solutions to the PDEs approximated based on polynomials. We develop an actor-critic RL algorithm to learn the optimal policy through interactions with the market environment. The algorithm carries out filtering to obtain the belief probability of the market regime and performs policy evaluation and policy gradient updates alternately. Empirical results demonstrate the advantages of our RL algorithm in relatively long-term investment problems over the classical control approach and an RL algorithm developed for the continuous-time mean-variance problem without considering regime switches.

The self-coordination mean-variance strategy in continuous time

The dynamic mean-variance portfolio selection problem is time inconsistent. In the literature, scholars try to derive the pre-committed strategy, the time consistent strategy and the self-coordination strategy. The pre-committed strategy only concern the global investment interest of the investor. The time consistent strategy only concerns the local investment interests of the investor, while the self-coordination strategy balances between the global investment interest and local investment interests of the investor. However, the self-coordination strategy is only studied for the discrete time mean-variance setting. We study the self-coordination strategy for the continuous time mean-variance setting in this paper. With the help of mean-field reformulation, we derive the analytical self-coordination mean-variance strategy and show that the pre-committed strategy and time consistent strategy are special cases of the self-coordination strategy.

Portfolio selection model using teaching learning-based optimization approach

&lt;p&gt;Portfolio selection is among the most challenging processes that have recently increased the interest of professionals in the area. The goal of mean-variance portfolio selection is to maximize expected return with minimizing risk. The Markowitz model was employed to solve the linear portfolio selection problem. However, due to numerous constraints and complexities, the problem is so critical that traditional models are insufficient to provide efficient solutions. Teaching learning-based optimization (TLBO) is a powerful population-based nature-inspired approach to solve optimization problems. This article presents a portfolio selection model using the TLBO approach to maximize the portfolio's Sharpe Ratio. The Sharpe ratio combines both expected return and risk. This algorithm model the natural teaching process of the classroom with two main phases, viz., teaching and learning. Performance analysis has been undertaken to investigate the suitability of TLBO based solution approach by comparing it with genetic algorithm (GA) and particle swarm optimization (PSO) on the real datasets, Deutscher Aktienindex (DAX) 100, Hang Seng 31, Standard and Poor’s (S&amp;amp;P) 100, financial times stock exchange (FTSE) 100, and Nikkei 225. The empirical results verify the superiority of the TLBO over GA and PSO.&lt;/p&gt;

Research on dynamic mean-variance portfolio selection

The covariance matrix of portfolio returns constructed by static mean-variance model will change with time, so the optimal portfolio with fixed weights may not be optimal. Based on the static mean-variance model, this paper introduces two new parameters of the length of dynamic historical period and holding period to construct a dynamic mean-variance model. Numerical analysis shows that the proposed dynamic portfolio strategy can achieve good returns.

Mean–variance portfolio selection under no-shorting rules: A BSDE approach

This paper revisits the mean–variance portfolio selection problem in continuous-time within the framework of short-selling of stocks is prohibited via backward stochastic differential equation approach. To relax the strong condition in Li et al. (Li et al. 2002), the above issue is formulated as a stochastic recursive optimal linear–quadratic control problem. Due to no-shorting rules (namely, the portfolio taking non-negative values), the well-known “completion of squares” no longer applies directly. To overcome this difficulty, we study the corresponding Hamilton–Jacobi–Bellman (HJB, for short) equation inherently and derive the two groups of Riccati equations. On one hand, the value function constructed via Riccati equations is shown to be a viscosity solution of the HJB equation mentioned before; On the other hand, by means of these Riccati equations and backward semigroup, we are able to get explicitly the efficient frontier and efficient investment strategies for the recursive utility mean–variance portfolio optimization problem.

Rehabilitating Mean–Variance Portfolio Selection: Theory and Evidence

Recent research has proven that the application of mean–variance portfolio selection is justified if, and only if, asset returns follow a skew-elliptical generalized location and scale (SEGLS) distribution. This irrefutably corrects the widespread fallacy that mean–variance analysis can be used only for portfolios with normally or symmetrically distributed constituents. To make this important finding accessible to a wide range of academics and practitioners, the authors of this article present it in a nontechnical form and additionally highlight that, under the SEGLS distribution and some mild axiomatic requirements, mean–variance analysis and many alternative mean-risk approaches deliver the same optimal portfolios. In a numerical study, they illustrate the key features of the novel SEGLS distribution. In an empirical study, they emphasize its practical relevance by gathering existing and providing new evidence in its favor.

Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

Trading Portfolio Strategy Optimization via Mean-Variance Model Considering Multiple Energy Derivatives

Energy retailers that sell energy at fixed prices are at risk of bankruptcy due to instantaneous fluctuations in wholesale electricity prices. Energy derivatives, e.g., electricity options, can be purchased by energy retailers then sold to customers as one potential risk-mitigation tool. A class of energy retailers that trade energy derivatives, including the electricity option, the carbon option and the green certificate, is considered in this paper. In terms of energy retailers, a strategy that can maximize the value of the purchased energy derivatives over a period of time and minimize the risk due to the stochastic price fluctuations is developed. Firstly, the dynamic prices of the electricity option as well as the carbon option are described by stochastic differential equations, and the dynamic prices of the green certificate are described by ordinary differential equations. Historical price data are used to obtain the parameters of both stochastic and ordinary differential equations by maximum likelihood estimation. Next, an investment portfolio is established as a mean-variance portfolio selection problem where the retailer maintains the satisfactory asset value and minimizes the risk simultaneously. Then, the problem is transformed into a stochastic optimal control problem which can be solved analytically by using the linear-quadratic method. Finally, the numerical simulations illustrate the feasibility of the proposed method.

Constrained mean-variance portfolio optimization for jump-diffusion process under partial information

This article studies a mean-variance portfolio selection problem for a jump-diffusion model, where the drift process is modulated by a continuous unobservable Markov chain. Since there is a constraint on wealth, we tackle this problem via the technique of martingale. We first investigate the full information case that the Markov chain can be observable, closed-form expressions not only for the optimal wealth process and optimal portfolio strategy but for the efficient frontier are derived. Then, by the filtering theory, we reduce the original partial information problem to a full information one, and the corresponding optimal results are obtained as well. Furthermore, if short selling is not allowed, we find that the solution in the full information case can be derived by transforming the problem into an equivalent one with constraint only on wealth, but this technique is not applicable anymore for the partial information case.

Mean-variance portfolio selection with random investment horizon

&lt;p style='text-indent:20px;'&gt;This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [&lt;xref ref-type="bibr" rid="b18"&gt;18&lt;/xref&gt;], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem.&lt;/p&gt;

Open-loop equilibrium strategy for mean-variance Portfolio selection with investment constraints in a non-Markovian regime-switching jump-diffusion model

&lt;p style='text-indent:20px;'&gt;This paper is devoted to study the open-loop equilibrium strategy for a mean-variance portfolio problem with investment constraints in a non-Markovian regime-switching jump-diffusion model. Specially, the investment strategies are constrained in a closed convex cone and all coefficients in the model are stochastic processes adapted to the filtration generated by a Markov chain. First, we provide a necessary and sufficient condition for an equilibrium strategy, which involves a system of forward and backward stochastic differential equations (FBSDEs, for short). Second, by solving these FBSDEs, we obtain a feedback representation of the equilibrium strategy. Third, we prove a theorem ensuring the almost everywhere uniqueness of the equilibrium solution. Finally, the results are applied to solve an example of the Markovian regime-switching model.&lt;/p&gt;

Optimal mean-variance portfolio selection with uncertain time horizon in a regime-switching market when asset returns are market path-dependent

Optimal mean-variance portfolio selection with uncertain time horizon in a regime-switching market when asset returns are market path-dependent

Open-loop equilibriums for a general class of time-inconsistent stochastic optimal control problems

&lt;p style='text-indent:20px;'&gt;This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward stochastic differential equations with jumps (FBSDEJs, for short), we derive two systems of integro-partial differential equations (IPDEs, for short). Then, we rigorously prove a verification theorem which provides a sufficient condition for open-loop equilibrium strategies. As special cases, a mean-variance portfolio selection problem and a time-inconsistent problem under non-exponential discounting are discussed.&lt;/p&gt;