Strategic portfolio management for long-term investments: An optimal control approach

In this thesis, a solution framework for the problem of strategic portfolio management for long-term investments is proposed which uses an optimal control approach. The aim of this work is to develop and apply methods of control engineering for solving the problem of multi-period portfolio optimization. The thesis introduces mathematical models in continuous and discrete time that describe the dynamics of assets. For these models, the corresponding feedback controllers are derived such that the objectives of the investors are optimized. In continuous time, the basic modelling and optimization frameworkis introduced and the problem of portfolio optimization is discussed with respect to other well-known control solutions. For asset price models where the expected returns are an affine function of economic factors, the portfolio optimization problem is solved analytically. The conditions for solving this problem are also derivedas well as the case where the economic factors are not directly observable. Since the analytical solutions depend on restrictive assumptions, such as no constraints on the control variables, a numerical method for solving the stochastic optimal control problems is derivedand its convergence is proved. The continuous-time methods are applied in two short case studies to German and US market data. In discrete time, modeis for the asset classes and the portfolio dynamics are introduced. The modelling of non-Gaussian asset distributions and the modelling of stochastic volatility (variance) is discussed. The problem of portfolio optimization in discrete time is stated and the conditions of optimality, i.e., the dynamic programming algorithm, are explained. Since for realistic assumptions, such as constraints, and large problem sizes, the solution of the dynamic programming algorithm is impractical and thus, two approximation methods are suggested. The first method is a suboptimal control strategy which uses the ideas from deterministic model predictive control. Model predictive control solves the problem of finding an optimal controller by consecutively solving the corresponding open-loop problem. The second method, called stochastic programming approximation, approximates the stochastic portfolio dynamicsby a finite number of scenarios and solves the feedback problem for the approximated dynamics. The two approximation methods are used to derive Solutions for portfolio optimizations for specific asset price modeis. With model predictive control, a Solution to the so-called linear Gaussian Factor model is derived and an extension to the model with time-varying and stochastic covariance raatrices is given. For portfolio problems with transaction costs and liabilities, a stochastic programming solution is explained. The methods for discrete-time portfolio optimizationsare applied in three case studies to real-world asset data. In the first case study, the model predictive control method is applied to a problemof maximizingthe expected returns subjectedto a so-called coherent risk measure constraint. The resultsof the out-of-sample test with mostly US stock market data show that the realized portfolio returns comply with the risk onstraint. In the second case study, the problem of construction a balanced fund, which invests in stocks, bonds, and cash, is solved. The portfolio optimization in this case study uses the analytical model predictive control solution where a heuristic is used to periodically select factors for the expected return predictions. The results of the computed portfolios show that the method outperforms suitable benchmarks with respect to absolute and risk-adjusted returns. In the third case study, the asset allocation problem for a Swiss fund is considered which invests domestically and in the EU markets. The fund gives a performance guarantee and is assumed to be large, such that it faces considerable transaction costs. The problem resembles the Situation that Swiss pension funds face for their asset allocation decisions. The case study shows that the computed strategy holds the p rtfolio values above the barrier of the Performance guarantee. Furthermore, the optimization adjusts the risk aversion depending on the distance between actual portfolio value and current minimum performance guarantee.