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Individual optimal pension allocation under stochastic dominance constraints

ANNALS OF OPERATIONS RESEARCH 2018年第1-2期260卷 255-291页

作者： Kopa, Milos Moriggia, Vittorio Vitali, Sebastiano Charles Univ Prague Fac Math & Phys Dept Probabil & Math Stat Sokolovska 83 Prague 18675 Czech Republic Univ Bergamo Dept Management Econ & Quantitat Methods Via Dei Caniana 2 I-24127 Bergamo Italy

An individual investor has to decide how to allocate his/her savings from a retirement perspective. This problem covers a long-term horizon. In this paper we consider a 40-year horizon formulating a multi-criteria multistage program with stochastic dominance constraints in an intermediate stage and in the final stage. As we are dealing with a real problem and we have formulated the model in cooperation with a commercial Italian bank, the intermediate stage corresponds to a possible withdrawal allowed by the Italian pension system. The sources of uncertainty considered are: the financial returns, the interest rate evolution, the investor's salary process and a considerable withdrawal event. We include a set of portfolio constraints according to the pension plan regulation. The objective of the model is to minimize the Average Value at Risk Deviation measure and to satisfy wealth goals. Three different wealth target formulations are considered: a deterministic wealth target (i.e. a comparison between the accumulated average wealth and a fixed threshold) and two stochastic dominance relations-the first order and the second order-introducing a benchmark portfolio and then requiring the optimal portfolio to dominate the benchmark. In particular, we prove that solutions obtained under stochastic dominance constraints ensure a safer allocation while still guaranteeing good returns. Moreover, we show how the withdrawal event affects the solution in terms of allocation in each of the three frameworks. Finally, the sensitivity and convergence of the stochastic solutions and computational issues are investigated.

关键词： Individual pension problem multistage stochastic programming stochastic dominance constraints Average value at risk deviation

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PRIMAL-DUAL AGGREGATION AND DISAGGREGATION FOR stochastic LINEAR-PROGRAMS

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MATHEMATICS OF OPERATIONS RESEARCH 1994年第4期19卷 893-908页

作者： WRIGHT, SE Department of Mathematics & Statistics Miami University Oxford Ohio 45056

A multistage stochastic linear program can be approximated by replacing the underlying information structure by a coarser structure. Given the ordinary Lagrangian for the original problem, this amounts to restricting both the primal and dual variables to be adapted to the coarser information structure. The resulting primal problem has the same form as the original, but with aggregated constraints and decisions. Mutual upper and lower bounds on the optimal values of the original and aggregated problems are obtained via partially aggregated problems formed by restricting only the primal variables or only the dual variables to the coarser structure. The introduction of the partially aggregated problems leads to a general disaggregation framework for developing heuristic approaches to solving the original problem.

关键词： multistage stochastic programming stochastic LINEAR programming AGGREGATION LAGRANGIAN DUALITY

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Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution

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ANNALS OF OPERATIONS RESEARCH 2013年第1期203卷 141-166页

作者： Tarhan, Bora Grossmann, Ignacio E. Goel, Vikas ExxonMobil Upstream Res Co Houston TX 77098 USA Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

In many planning problems under uncertainty the uncertainties are decision-dependent and resolve gradually depending on the decisions made. In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete time horizon. In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the model are not prespecified but change as a function of the decisions made. Furthermore, planning problems consist of several scenario subproblems where each subproblem is modeled as a nonconvex mixed-integer nonlinear program. We propose a solution strategy that combines global optimization and outer-approximation in order to optimize the planning decisions. We apply this generic problem structure and the proposed solution algorithm to several planning problems to illustrate the efficiency of the proposed method with respect to the method that uses only global optimization.

关键词： Decision making under uncertainty Decision dependent uncertainty Gradual uncertainty resolution multistage stochastic programming Non-convex mixed integer nonlinear program Global optimization Outer-approximation Oil or gas field exploration Synthesis of process networks

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Structure of risk-averse multistage stochastic programs

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OR SPECTRUM 2015年第3期37卷 559-582页

作者： Dupacova, Jitka Kozmik, Vaclav Charles Univ Prague Fac Math & Phys Dept Probabil & Math Stat Prague Czech Republic

We deal with risk-averse multistage stochastic programs with coherent risk measures such as multiperiod extensions of conditional value at risk or polyhedral risk measures. Their basic properties are discussed and applied to scenario-based input data. Using the contamination technique we quantify the influence of changes in the structure of the scenario-based approximation to the optimal value of the problem. stochastic dual dynamic programming algorithm is used to provide illustrative numerical comparisons for different choices of risk measures and changes of input data for a simple multistage risk-averse stock allocation problem with scenario trees based on log-normal distribution of the asset returns.

关键词： multistage stochastic programming Multiperiod risk measures stochastic dual dynamic programming Contamination

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Stability of multistage stochastic programs incorporating polyhedral risk measures

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OPTIMIZATION 2008年第2期57卷 295-318页

作者： Eichhorn, Andreas Roemisch, Werner Humboldt Univ Dept Math Berlin Germany

We analyse stability aspects of linear multistage stochastic programs with polyhedral risk measures in the objective. In particular, we consider sensitivity of the optimal value with respect to perturbations of the underlying stochastic input process. An existing stability result for multistage stochastic programs with expectation objective is carried forward to the case of polyhedral risk-averse objectives. Beside Lr-distances these results also involve filtration distances of the perturbations of the stochastic process. We discuss additional requirements for the polyhedral risk measures such that the problem dependent filtration distances can be bounded by problem independent ones. Stability and such bounds are the basis for scenario tree approximation techniques used in practical problem solving.

关键词： multistage stochastic programming optimization quantitative stability filtration distance polyhedral risk measures multiperiod risk functionals

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Multi-period portfolio selection with interval-based conditional value-at-risk

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ANNALS OF OPERATIONS RESEARCH 2024年 1-39页

作者： Gomez, Alvaro A. Consigli, Giorgio Liu, Jia Khalifa Univ Sci & Technol Dept Math CCMS POB 127788 Abu Dhabi 2022010 U Arab Emirates Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China

We propose a multi-period mean-risk portfolio model based as a risk measure on the interval conditional value at risk (ICVaR). The ICVaR was introduced in Liu et al. (Ann Op Res 307:329-361, 2021) in a strict relationship with second-order stochastic dominance and adopted as risk measure in the formulation of a static portfolio optimization problem: in this article we reconsider its key properties and specify a multistage portfolio model based on the trade-off between expected wealth and terminal ICVaR. The definition of this risk measure depends on a reference point, that by discriminating between contiguous stochastic dominance orders motivated in Liu et al. (2021) the introduction of interval stochastic dominance (ISD) of the first and second-order specifically in a financial context. We develop from there in this article and present a set of results that help characterizing rigorously the relationship between the solution of the multistage stochastic programming portfolio problem and the underlying ISD principles. An extended set of computational results is presented to validate in- and out-of-sample a set of mathematical results and the modeling framework over the 2021-2022 period.

关键词： multistage stochastic programming stochastic dominance Interval conditional value-at-risk Multi-period mean-risk model

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Medium-term planning for thermal electricity production

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OR SPECTRUM 2014年第3期36卷 723-759页

作者： Kovacevic, Raimund M. Paraschiv, Florentina Univ Vienna Dept Stat & Decis Support Syst A-1010 Vienna Austria Univ St Gallen Inst Operat Res & Computat Finance CH-9000 St Gallen Switzerland

In the present paper, we present a mid-term planning model for thermal power generation which is based on multistage stochastic optimization and involves stochastic electricity spot prices, a mixture of fuels with stochastic prices, the effect of CO emission prices and various types of further operating costs. Going from data to decisions, the first goal was to estimate simulation models for various commodity prices. We apply Geometric Brownian motions with jumps to model gas, coal, oil and emission allowance spot prices. Electricity spot prices are modeled by a regime switching approach which takes into account seasonal effects and spikes. Given the estimated models, we simulate scenario paths and then use a multiperiod generalization of the Wasserstein distance for constructing the stochastic trees used in the optimization model. Finally, we solve a 1-year planning problem for a fictitious configuration of thermal units, producing against the markets. We use the implemented model to demonstrate the effect of CO prices on cumulated emissions and to apply the indifference pricing principle to simple electricity delivery contracts.

关键词： multistage stochastic programming Tree generation Electricity production Modeling commodity spot prices

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The optimal harvesting problem under price uncertainty: the risk averse case

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ANNALS OF OPERATIONS RESEARCH 2017年第2期258卷 479-502页

作者： Pagnoncelli, Bernardo K. Piazza, Adriana Univ Adolfo Ibanez Escuela Negocios Diagonal Torres 2640 PenalolenOficina 533 C Santiago Chile Univ Tecn Federico Santa Maria Dept Matemat Ave Espana 1680Casilla 110-5 Valparaiso Chile

We study the exploitation of a one species, multiple stand forest plantation when timber price is governed by a stochastic process. Our model is a stochastic dynamic program with a weighted mean-risk objective function, and our main risk measure is the Conditional Value-at-Risk. We consider two stochastic processes, geometric Brownian motion and Ornstein-Uhlenbeck: in the first case, we completely characterize the optimal policy for all possible choices of the parameters while in the second, we provide sufficient conditions assuring that harvesting everything available is optimal. In both cases we solve the problem theoretically for every initial condition. We compare our results with the risk neutral framework and generalize our findings to any coherent risk measure that is affine on the current price.

关键词： multistage stochastic programming Optimal harvesting Forestry Coherent risk measures

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Assessment of risk-averse policies for the long-term hydrothermal scheduling problem

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2017年第1期8卷 103-125页

作者： Larroyd, Paulo Vitor de Matos, Vitor Luiz Finardi, Erlon Cristian Univ Fed Santa Catarina Florianopolis SC Brazil Plan4 Florianopolis SC Brazil

The goal of the long-term hydrothermal scheduling (LTHS) problem is to determine an optimal policy that minimises the expected operational cost over a multi-annual planning horizon. In this problem, inflows are naturally random;thus, the development of policies requires the use of specialised techniques such as stochastic optimization algorithms. Although the optimal policy defined by means of the expected cost is economically efficient, the associated decisions can incur a high risk of energy deficit. To overcome such disadvantages, one alternative is to include a risk-measure approach in the LTHS modeling. In this study, we compared two different risk-measure strategies applied to the LTHS problem: (i) a convex combination between the conditional value at risk (CVaR) and the expected operational cost, (ii) a reservoir risk-curve. To accomplish the comparison, we consider the Brazilian power system with a 5-year planning horizon discretized in monthly stages. The policies supplied by the risk-averse strategies are simulated in a set of synthetic inflow scenarios. Thus, the results are obtained in terms of the expected long-term hydrothermal decisions, such as the total operational cost and the reservoir storage. In summary, the CVaR-based policies provided better operational results than the risk-curve one.

关键词： multistage stochastic programming Long-term hydrothermal scheduling CVaR Risk-curve

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On the number of stages in multistage stochastic programs

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ANNALS OF OPERATIONS RESEARCH 2020年第2期292卷 581-603页

作者： Pantuso, Giovanni Boomsma, Trine K. Univ Copenhagen Dept Math Sci Univ Pk 5 DK-2100 Copenhagen Denmark

multistage stochastic programs serve to make sequential decisions conditional on a gradual realization of some stochastic process. The progressive arrival of new information divides a problem into stages. As the number of stages increases, however, the applicability of stochastic programming is halted by the curse of dimensionality. A commonly used approximation is obtained by replacing the random parameters by their expected values, which results in a problem with fewer stages. The present paper suggests metrics to support the choice of the number of stages: The value of an extended expected value (EV) problem which accounts for stochastic approximations, the Expected result of using the expected value solution (EEV), the value of the stochastic solution, and the values of two Wait-and-See (WS) approximations. We show that for linear minimization problems with random right-hand-side, the value of the EV problem provides a lower bound that improves with the number of stages. The same holds for the WS approximations for general linear minimization problems and with one of the approximations improving the EV bound. In contrast, we show that the upper bound provided by the EV solution may not improve with the number of stages. Finally, we define the marginal benefit of including an additional stage in an EV approximation and demonstrate how to use it in a heuristic. We apply our approach to a hedging problem and confirm that increasing the number of stages does not necessarily foster better decisions.

关键词： multistage stochastic programming Value of the stochastic solution Bounds Optimization under uncertainty

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