Long-term individual financial planning under stochastic dominance constraints
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Long-term individual financial planning under stochastic dominance constraints Giorgio Consigli1
· Vittorio Moriggia1 · Sebastiano Vitali1,2
© Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract We analyse an optimal goal-based households’ asset-liability management problem characterised by a real estate target and a retirement goal over a long-term planning horizon. The problem is formulated as a multistage stochastic program and we evaluate the impact of second order stochastic dominance (SSD) constraints on different specifications of a family objective function and with respect to three alternative benchmark policies. We define a stochastic linear program in which the SSD constraints are based on a double stochastic matrix, whose effectiveness in determining the decision maker strategies is studied in a case study developed in the second part of the article. We show that depending on the adopted benchmark policy, SSD constraints even if binding far on the planning horizon, may influence the root node investment decision and affect both the investment and the liability optimal policies. Based on an extended computational study we analyse under which conditions and problem formulation, an SSD condition may also imply first order stochastic dominance (FSD). Finally we analyse the relationship between the specification of a minimum shortfall objective with respect to the goals and the introduced SSD constraints at the terminal horizon. Keywords Dynamic stochastic programming · Stochastic dominance · Asset-liability management · Goal-based investing · Life cycle policy · Consumption-investment trade-off JEL Classification C44 · C61 · C63 · D15 · G11 · G22 · G41
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Giorgio Consigli [email protected] Vittorio Moriggia [email protected] Sebastiano Vitali [email protected]
1
Department of Management, Economics and Quantitative Methods, University of Bergamo, Via dei Caniana 2, 24 127 Bergamo, Italy
2
Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic
123
Annals of Operations Research
1 Introduction We consider in this work a family’s dynamic asset-liability management (ALM) problem over a long-term planning horizon formulated as a multistage stochastic program (MSP) in which the decision maker seeks jointly an expected wealth maximisation objective and the minimisation of the shortfall with respect to an intermediate and a terminal retirement goal. Both goals are stochastic and the decision problem is formulated taking the household’s long term financial safety into account. The attainability of each goal is subject to an uncertainty generated by asset returns and liability costs and we formulate the optimization problem with second order stochastic dominance (SSD) constraints. We analyse the implications of SSD constraints on a canonical household investment-consumption problem in which, due to the intermediate real-estate target, the solution takes the fo
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