Multi-stage Portfolio Optimization Research Articles

Optimal investment policy in a multi-stage problem with bankruptcy and stage-by-stage probability constraints

ABSTRACT The present paper studies a multi-stage portfolio optimization problem with bankruptcy and stage-by-stage value at risk (VaR) constraints that impose boundary for probability of the percentage of the investor's capital shortfall at each stage. The goal function is the mean value of final investor's capital. Making use of the stage-by-stage VaR constraints and a multivariate normal model for rates of return, the method of dynamic programming is applied. Due to peculiarities of this optimal control problem of the Markov chain with a set of absorbing states, an optimal investment policy turns out to be a relatively simple policy. More exactly, at each stage optimal portfolio depends only on the number of stage, but not on the value of current investor's capital. The initial problem is reduced to a sequence of one-stage portfolio optimization problems. Analysis of such one-stage problem is mainly based on known results, providing sufficient and necessary conditions for fulfilment of Slater's constraint qualification, as well as conditions for optimality. In addition, we extend the obtained results to a non-normality situation by use of elliptical distributions.

Multistage portfolio optimization with multivariate dominance constraints

In this article we focus on multistage portfolio optimization problem with usage of multivariate stochastic dominance constraints. The first part of the work is devoted to the theoretical background needed for establishing the optimization problem. We provide a general approach to multivariate stochastic dominance, we mainly recall basic definitions and several statements that are relevant for portfolio optimization, and describe an algorithm for detecting multivariate stochastic dominance of two random vectors with discrete distributions. The main part of the work introduces multivariate stochastic dominance constraints in multistage portfolio optimization problem. We compare obtained results with traditional model which employs univariate first order stochastic dominance constraints at each stage.

Using genetic algorithm to support clustering-based portfolio optimization by investor information

A clustering-based portfolio optimization scheme that employs a genetic algorithm (GA) based on investor information for active portfolio management is presented. Whereas numerous studies have investigated trading behaviors, investor performance, and portfolio investment strategies, few works have developed investment strategies based on investor information. This study is conducted in two phases. First, a basket of portfolio (i.e., a collection of stocks held in individual portfolios) is developed through a cluster analysis of investor information. A GA is then employed to optimize the weights of the selected stocks. And the optimized portfolio is rebalanced to get excess return. It is concluded that the proposed multistage portfolio optimization scheme for active portfolio management generates superior results than previously proposed methods for the Korean stock market.

Multistage portfolio optimization with stocks and options

We develop a multistage portfolio optimization model that utilizes options for mitigating market risk in a dynamic setting. Due to the key role of scenarios in the quality of investment decisions, a new scenario generation method is proposed that characterizes the dynamic behavior of asset returns. This methodology takes the dependence structure of different asset returns into account, and also considers serial correlations of each of the asset returns. Moreover, it preserves marginal distributions of asset returns. Also, it precludes arbitrage opportunities. To investigate the role of options, we implement the scenario generation method on a set of stocks selected from the New York Stock Exchange. Results show the high performance of the proposed scenario generation method. Afterwards, the generated set of scenarios is used as the uncertainty set for the multistage portfolio optimization model. Static and dynamic assessments are used for measuring the performance of options in mitigating market risks and generating additional returns. Finally, backtesting simulations are used for assessing different trading strategies of options.

Solving the multi-stage portfolio optimization problem with a novel particle swarm optimization

Solving the multi-stage portfolio optimization (MSPO) problem is very challenging due to nonlinearity of the problem and its high consumption of computational time. Many heuristic methods have been employed to tackle the problem. In this paper, we propose a novel variant of particle swarm optimization (PSO), called drift particle swarm optimization (DPSO), and apply it to the MSPO problem solving. The classical return-variance function is employed as the objective function, and experiments on the problems with different numbers of stages are conducted by using sample data from various stocks in S&P 100 index. We compare performance and effectiveness of DPSO, particle swarm optimization (PSO), genetic algorithm (GA) and two classical optimization solvers (LOQO and CPLEX), in terms of efficient frontiers, fitness values, convergence rates and computational time consumption. The experiment results show that DPSO is more efficient and effective in MSPO problem solving than other tested optimization tools.

A DSS for stochastic multistage portfolio optimization in the Mexican market

We present the main elements for a decision support system for portfolio management in the Mexican market, includingthe financial investments consideration for a database, the uncertainty representation in scenario trees and the requirements for aportfolio optimization model. We used a stochastic programming approach to formulate the multistage optimization model, modifiedwith new constraints and solved it with a Simulated Annealing procedure. The scenario tree was generated by a simulation andclustering process.