Stochastic Dominance Constraints Research Articles

A neural network framework for portfolio optimization under second-order stochastic dominance

Traditional portfolio optimization strategies often rely on statistical methods and linear programming tools to achieve a balance between return and risk. Despite their usefulness for portfolio optimization, they cannot efficiently capture the specific differences and complexity of real-world financial markets. Several modern approaches attempt to overcome these limitations by using nonlinear models, machine learning, and advanced risk measures. In this study, we propose a novel strategy for optimizing portfolios that incorporates second-order stochastic dominance constraints and solves them with neural networks. we show that portfolios subject to second-order stochastic dominance constraints outperform their traditional counterparts, especially in tail-risk situations.

Adjustable light robust optimization with second order stochastic dominance constraints

Robust optimization suffers from excessive conservatism and infeasibility due to stringent requirements on all constraints within the uncertainty set, rendering robust solutions impractical. The light robust approach has been proposed to mitigate these challenges. This method aims to identify a solution that minimizes the weighted sum of all constraint violations while adhering to a predetermined limit on the deterioration of expected return. Drawing inspiration from light robustness, our paper introduces the adjustable light robust optimization models with second-order stochastic dominance constraints. We empirically examine their feasibility, out-of-sample performance, and the dynamic trade-off between return and robustness.

Investments in transmission lines and storage units considering second-order stochastic dominance constraints

Increasing intermittent renewable generation to meet the climate goals entails a deep transformation of current power systems. The transmission system must adapt to ensure a rapid and flexible response to the changes in the energy flows. Flexibility can be provided by reinforcing the interconnection among all the market agents and/or by installing facilities with fast response to the changes. In this work, we study the investment problem of a central planner that seeks to expand the transmission network and install storage units considering decarbonizing measures. We propose a two-stage stochastic problem with uncertainty on the demand growth and including representative days to characterize the hourly demand and renewable power variability. To obtain better expansion strategies according to a limit on the carbon emissions, second-order stochastic dominance constraints are imposed. Numerical analyses based on the power system of the Canary island (Spain) are provided. The results show that to install storage units is key to efficiently integrate renewable generation. The investments in the transmission system are mostly in lower-voltage lines. The formulation with stochastic dominance constraints results in higher second-stage investments, allowing a better adaptation to the demand growth evolution.

Portfolio reshaping under 1st-order stochastic dominance constraints by the exact penalty function methods

The paper studies a financial portfolio selection problem under 1st-order stochastic dominance constraints. These constraints constitute lower bounds on the return profile of the portfolio. In particular, they allow searching for a better portfolio than some reference portfolio by comparing their cumulative distribution functions. Candidate objective functions are the average return, a value at risk, or the average value at risk. The optimization problems obtained are computationally hard because of possibly non-convex constraints and possibly discontinuous objective functions. In the case of a discrete distribution of the return, we develop numerical procedures to solve the problem. The proposed approach uses new exact penalty functions to tackle with the 1st-order stochastic dominance constraints. The resulting penalized objective function is further optimized be the stochastic successive smoothing method as a local optimizer within some branch and bound global optimization scheme. The approach is numerically and graphically illustrated on small portfolio selection problems up to dimension 10.

Multistage stochastic dominance: an application to pension fund management

AbstractA pension fund manager typically decides the allocation of the pension fund assets taking into account a long-term sustainability goal. Many asset and liability management models, in the form of multistage stochastic programming problem, have been proposed to help the pension fund manager to define the optimal allocation given a multi-objective function. The recent literature proposes univariate stochastic dominance constraints to guarantee that the optimal strategy is able to stochastically dominate a benchmark portfolio. In this work we extend previous results (i) considering alternative types of multivariate stochastic dominance that appear more suitable in a multistage framework, (ii) proposing a way to measure the economic cost of introducing stochastic dominance constraints, (iii) proposing a sort of augmented stochastic dominance through a safety margin. Numerical results show the difference between the alternative ways to interpret and apply the multivariate stochastic dominance. These results are evaluated thanks to the proposed economic cost of the stochastic dominance constraints and either in presence or not of a safety margin.

A financial modeling approach to industry exchange-traded funds selection

This study uses a comprehensive approach to optimize the portfolio allocation to equity sector Exchange Traded Funds. We combine data on the market prices of options written on the funds, the Heston stochastic volatility model, risk premium transformation, copulas, and optimization with stochastic dominance constraints. This comprehensive strategy provides significant performance out-of-sample gains relative to the passive and active alternative strategies, both before and after accounting for risk and transaction costs. Our findings point at market inefficiencies that can be exploited using sector funds, past public data, and blending multiple methods.

Robust reward-risk performance measures with weakly second-order stochastic dominance constraints

Robust reward-risk performance measures with weakly second-order stochastic dominance constraints

Data-Driven Optimization with Distributionally Robust Second Order Stochastic Dominance Constraints

This paper presents the first comprehensive study of a data-driven formulation of the distributionally robust second order stochastic dominance constrained problem (DRSSDCP) that hinges on using a type-1 Wasserstein ambiguity set. It is, furthermore, for the first time shown to be axiomatically motivated in an environment with distribution ambiguity. We formulate the DRSSDCP as a multistage robust optimization problem and further propose a tractable conservative approximation that exploits finite adaptability and a scenario-based lower bounding problem. We then propose the first exact optimization algorithm for this DRSSDCP. We illustrate how the data-driven DRSSDCP can be applied in practice on resource-allocation problems with both synthetic and real data. Our empirical results show that, with a proper adjustment of the size of the Wasserstein ball, DRSSDCP can reach acceptable out-of-sample feasibility yet still generating strictly better performance than what is achieved by the reference strategy.

Distributionally robust portfolio optimization with second-order stochastic dominance based on wasserstein metric

In portfolio optimization, we may be dealing with misspecification of a known distribution, that stock returns follow it. The unknown true distribution is considered in terms of a Wasserstein-neighborhood of P to examine the tractable formulations of the portfolio selection problem. This study considers a distributionally robust portfolio optimization problem with an ambiguous stochastic dominance constraint by assuming the unknown distribution of asset returns. The objective is to maximize the worst-case expected return and subject to an ambiguous second-order stochastic dominance constraint. The expected return robustly stochastically dominates the benchmark in the second order over all possible distributions within an ambiguity set. It is also shown that the Wasserstein-moment ambiguity set-based distributionally robust portfolio optimization can be reduced to a semidefinite program and second-order conic programming. We use a cutting plane to solve our second-order stochastic dominance constraint portfolio optimization problem with ambiguity sets based on the Wasserstein metric. Then we decompose this class of distributionally robust portfolio optimization into semi-infinite programming and apply the cutting surface method to solve it. The captured optimization programs are applied to real-life data for more efficient comparison. The problems are examined in depth using the optimal solutions of the optimization programs based on the different setups.

Short Communication: Minimal Quantile Functions Subject to Stochastic Dominance Constraints

Short Communication: Minimal Quantile Functions Subject to Stochastic Dominance Constraints

Semiparametric modelling of two-component mixtures with stochastic dominance.

In this work, we studied a two-component mixture model with stochastic dominance constraint, a model arising naturally from many genetic studies. To model the stochastic dominance, we proposed a semiparametric modelling of the log of density ratio. More specifically, when the log of the ratio of two component densities is in a linear regression form, the stochastic dominance is immediately satisfied. For the resulting semiparametric mixture model, we proposed two estimators, maximum empirical likelihood estimator (MELE) and minimum Hellinger distance estimator (MHDE), and investigated their asymptotic properties such as consistency and normality. In addition, to test the validity of the proposed semiparametric model, we developed Kolmogorov–Smirnov type tests based on the two estimators. The finite-sample performance, in terms of both efficiency and robustness, of the two estimators and the tests were examined and compared via both thorough Monte Carlo simulation studies and real data analysis.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10463-022-00835-5.

Distributionally robust optimization with multivariate second-order stochastic dominance constraints with applications in portfolio optimization

In this paper, we study the stochastic optimization problem with multivariate second-order stochastic dominance (MSSD) constraints where the distribution of uncertain parameters is unknown. Instead, only some historical data are available. Using the Wasserstein metric, we construct an ambiguity set and develop a data-driven distributionally robust optimization model with multivariate second-order stochastic dominance constraints (DROMSSD). By utilizing the linear scalarization function, we transform MSSD constraints into univariate constraints. We present a stability analysis focusing on the impact of the variation of the ambiguity set on the optimal value and optimal solutions. Moreover, we carry out quantitative stability analysis for the DROMSSD problems as the sample size increases. Specially, in the context of the portfolio, we propose a convex lower reformulation of the corresponding DROMSSD models under some mild conditions. Finally, some preliminary numerical test results are reported. We compare the DROMSSD model with the sample average approximation model through out-of-sample performance, certificate and reliability. We also use real stock data to verify the effectiveness of the DROSSM model.

Multi-stage portfolio selection problem with dynamic stochastic dominance constraints

Multi-stage portfolio selection problem with dynamic stochastic dominance constraints

Optimal portfolio choice for higher-order risk averters

The effects of higher-order risk aversion on optimal cross-sectional portfolio choice are investigated using portfolio optimization with Stochastic Dominance constraints. Tractable sufficient conditions for higher-degree dominance are introduced that take the form of a system of linear inequalities. Existing studies of active equity industry rotation are extended from lower degrees to higher degrees of dominance. Fourth-degree dominance assumes that investors are ‘prudent’ and ‘temperate’ and therefore like skewness and dislike kurtosis. Using this dominance criterion leads to superior out-of-sample investment performance, by allowing for more concentration in recent winner industries which tend to show persistent positive abnormal returns and a favorable higher-order risk profile due to the industry-level price momentum effect.

Analysing decarbonizing strategies in the European power system applying stochastic dominance constraints

In this paper we develop an analysis of the efficiency of the expansion strategies to be followed to attain the emissions targets established by the European Commission in the Energy Roadmap 2050. A multi-stage investment model in generating and storage capacity from the point of view of a central planner is presented, considering long-term uncertainties in the decision-making process, such as the demand growth and the investment and fuel costs, and short-term variability. To evaluate the wellness of the expansion strategies according to the CO2 emissions generated and the total cost, second-order stochastic dominance constraints are introduced in the model. This approach allows to obtain better expansion strategies enforcing acceptable distributions of CO2 emissions. The numerical study is carried out considering the case of the European power system. The predictions and suggestions made by the European Commission towards 2050 are the basis to define the benchmark solutions, whose outcomes are analysed. The results obtained from this study highlight that a renewable capacity of at least 2900 GW is needed to attain a net zero CO2 emission European power system. The strategy based on carbon capture and storage does not reduce effectively CO2 emissions while it represents an expensive alternative. Including stochastic dominance in the optimization model allows to obtain less expensive alternative expansion strategies with comparatively lower CO2 emissions in the worst scenarios.

A two-component nonparametric mixture model with stochastic dominance

In this paper, we introduced a new two-component nonparametric mixture model with a stochastic dominance constraint, a model arising naturally from many genetic studies. For this model, we proposed and studied two estimations. The first one is based on cumulative distribution functions with use of the stochastic dominance inequality, while the second one is a maximum likelihood estimation of the multinomial approximation of the model. For both methods, we not only proved their consistency but also examined their finite-sample performance through simulation studies. Our numerical studies showed that both methods work equivalently well. To demonstrate their implementation, we applied them to two real datasets.

Expected Utility Maximization with Stochastic Dominance Constraints in Complete Markets

The problem of expected utility maximization with stochastic dominance constraints in complete markets is studied. In the quantile formulation, i.e., changing the decision variable of the problem from a random variable to its quantile function, the problem with a first-order stochastic dominance constraint is easy and can be solved explicitly. For the problem with a second-order stochastic dominance constraint, the optimal solution is characterized explicitly in terms of the solution of a dual problem, which interestingly can be regarded as a problem of two-person efficient risk sharing. Moreover, the optimal solution of the problem of efficient risk sharing is characterized fully and, in some special cases, has closed form.

Pension fund management with investment certificates and stochastic dominance

This paper considers an extension of the common asset universe of a pension fund to investment certificates. Investment certificates are a class of structured products particularly interesting for their special payoff structures and they are acquiring relevancy in the worldwide markets. In fact, some subclasses of certificates offer loss protection and show high liquidity and, thus, they can be very appreciated by pension fund managers. We consider the problem of a pension fund manager who has to implement an Asset and Liability Management model trying to achieve a long-term sustainability. Therefore, we formulate a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. We propose a technique to price highly structured products such as investment certificates on a discrete scenario tree. Finally, we solve the investment problem considering some investment certificate types both in term of payoff structure and protection level, and we test whether they are preferred or not to standard hedging contract such as put options. Moreover, we test the inclusion of first-order and second-order stochastic dominance constraints on multiple stages with respect to a benchmark portfolio. Numerical results show that the portfolio composition reacts to the inclusion of the stochastic dominance constraints, and that the optimal portfolio is efficiently able to reach several targets such as liquidity, returns, sponsor’s extraordinary contribution and funding gap.

On distributionally robust optimization problems with k-th order stochastic dominance constraints induced by full random quadratic recourse

In this paper, we consider the optimization problems with k-th order stochastic dominance constraint on the objective function of the two-stage stochastic programs with full random quadratic recourse. By establishing the Lipschitz continuity of the feasible set mapping under some pseudo-metric, we show the Lipschitz continuity of the optimal value function and the upper semicontinuity of the optimal solution mapping of the problem. Furthermore, by the Hölder continuity of parameterized ambiguity set under the pseudo-metric, we demonstrate the quantitative stability results of the feasible set mapping, the optimal value function and the optimal solution mapping of the corresponding distributionally robust problem.

A simple proof of strong duality in the linear persuasion problem

We provide a simple proof of strong duality for the linear persuasion problem. The duality is established in Dworczak and Martini (2019), under slightly stronger assumptions, using techniques from the literature on optimization with stochastic dominance constraints and several approximation arguments. We provide a short, alternative proof that is based on a direct argument to show the existence of optimal price functions, and on switching the roles of the primal and the dual to show that there is no duality gap.