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dynamic stochastic programming for asset-liability management

ANNALS OF OPERATIONS RESEARCH 1998年 81卷 131-161页

作者： Consigli, G Dempster, MAH Univ Cambridge Judge Inst Management Studies Cambridge CB2 1AG England

Multistage stochastic programming - in contrast to stochastic control - has found wide application in the formulation and solution of financial problems characterized by a large number of state variables and a generally low number of possible decision stages. The literature on the use of multistage recourse modelling to formalize complex portfolio optimization problems dates back to the early seventies, when the technique was first adopted to solve a fixed income security portfolio problem. We present here the CALM model, which has been designed to deal with uncertainty affecting both assets (in either the portfolio or the market) and liabilities (in the form of scenario dependent payments or borrowing costs). We consider as an instance a pension fund problem in which portfolio rebalancing is allowed over a long-term horizon at discrete time points and where liabilities refer to five different classes of pension contracts. The portfolio manager, given an initial wealth, seeks the maximization of terminal wealth at the horizon, with investment returns modelled as discrete state random vectors. Decision vectors represent possible investments in the market and holding or selling assets in the portfolio, as well as borrowing decisions from a credit line or deposits with a bank. Computational results are presented for a set of IO-stage portfolio problems using different solution methods and libraries (OSL, CPLEX, OBI). The portfolio problem, with an underlying vector data process which allows up to 2688 realizations at the 10-year horizon, is solved on an IBM RS6000/590 for a set of twenty-four large-scale test problems using the simplex and barrier methods provided by CPLEX (the latter for either linear or quadratic objective), the predictor/corrector interior point method provided in OBI, the simplex method of OSL, the MSLiP-OSL code instantiating nested Benders decomposition with subproblem solution using OSL simplex, and the current version of MSLiP.

关键词： asset-liability portfolio management pension fund management dynamic stochastic programming linear programming quadratic programming simplex method interior point method nested Benders decomposition

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dynamic stochastic programming for asset allocation problem

Dynamic stochastic programming for asset allocation problem

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IEEE International Conference on Industrial Engineering and Engineering Management

作者： Song, Haiqing Huang, Huei-Chuen Natl Univ Singapore Dept Syst & Ind Engn Singapore Singapore Sun Yat Sen Univ Lingnan Coll Guangzhou Peoples R China

ISBN: (纸本)9781424415281

Asset allocation is an important decision problem in financial planning. In this paper, we study the multistage dynamic asset allocation problem which an investor is allowed to reallocate its wealth among a set of assets over finite discrete decision points, in which the stochastic return rates of the assets follow a Markov chain with nonstationary transition probabilities. The objective is to maximize the utility of the wealth at the end of the planning horizon where the utility of the wealth follows a general piecewise linear and concave function. Transaction costs are considered. We formulate the problem with a dynamic stochastic programming model and develop a method that decomposes the problem into stage-based subproblems to solve it. The main advantage of this method is that it provides a computationally tractable tool to deal with the dynamic asset allocation problem of long planning horizon.

关键词： asset allocation dynamic stochastic programming portfolio management

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Optimal insurance portfolios risk-adjusted performance through dynamic stochastic programming

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COMPUTATIONAL MANAGEMENT SCIENCE 2018年第3-4期15卷 599-632页

作者： Consigli, Giorgio Moriggia, Vittorio Vitali, Sebastiano Mercuri, Lorenzo Univ Bergamo Dept Management Econ & Quantitat Methods Via Caniana 2 I-24127 Bergamo Italy Charles Univ Prague Fac Math & Phys Dept Probabil & Math Stat Sokolovska 83 Prague 18675 Czech Republic Univ Milan Dept Econ Management & Quantitat Methods Via Conservatorio 7 I-20122 Milan Italy

The practical adoption of the Solvency II regulatory framework in 2016, together with increasing property and casualty (PC) claims in recent years and an overall reduction of treasury yields across more developed financial markets have profoundly affected traditional risk management approaches by insurance institutions. The adoption of firm-wide risk capital methodologies to monitor the companies' overall risk exposure has further consolidated the introduction of risk-adjusted performance measures to guide the management medium and long-term strategies. Relying on a dynamic stochastic programming formulation of a 10 year asset-liability management (ALM) problem of a PC company, we analyse in this article the implications on capital allocation and risk-return trade-offs of an optimization problem developed for a global insurance company based on a pair of risk-adjusted return functions. The analysis is relevant for any institutional investor seeking a high risk-adjusted performance as for regulators in their structuring of stress-tests and effective regulatory frameworks. The introduction of the concept of risk capital, or economic capital, in the definition of medium and long term insurance strategies poses a set of modeling and methodological issues tackled in this article. Of particular interest is the study of optimal ALM policies under different assets' correlation assumptions. From a computational viewpoint it turns out that, depending on the assumed correlation matrix, the stochastic program is linear or of second order conic type. A case study from a real-world company development is presented to highlight the effectiveness of applied stochastic programming in capturing complex risk and return dynamics arising in modern corporate finance and lead to an efficient long-term financial allocation process.

关键词： Property and casualty liabilities dynamic stochastic programming Risk capital allocation Return on risk-adjusted capital Surplus investment return

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Galerkin methods in dynamic stochastic programming

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OPTIMIZATION 2010年第3期59卷 339-354页

作者： Koivu, Matti Pennanen, Teemu Aalto Univ Dept Math & Syst Anal FI-00076 Aalto Finland Finnish Financial Supervisory Author FIN-00101 Helsinki Finland

The Galerkin method is a classical technique for approximating infinite-dimensional optimization problems with finite-dimensional ones. When applied to convex multistage stochastic programmes, it yields computationally attractive alternatives to scenario tree-based discretizations. We describe its implementations for dynamic portfolio optimization problems and report some encouraging numerical results.

关键词： dynamic stochastic programming Galerkin method basis strategies convexity

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On stochastic programming ii: dynamic problems under risk∗

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stochastics 1988年第1期25卷 15-42页

This paper surveys recent work on dynamic stochastic programming problems and their applications. New results are included on the measurability and interpretation-in terms of the expected value of perfect information (EVPI)-of the dual multiplier processes corresponding to these problems. A final section reports preliminary computational experiments with algorithms for 2-stage problems

关键词： dynamic stochastic programming discrete time stochastic control expected value of perfect information Lagrangean decomposition computational techniques

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Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第3期234卷 743-750页

作者： Rudloff, Birgit Street, Alexandre Valladao, Davi M. Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA Pontif Catholic Univ Rio de Janeiro PUC Rio Dept Elect Engn BR-22451900 Gavea Rio de Janeiro RJ Brazil Pontif Catholic Univ Rio de Janeiro PUC Rio Dept Ind Engn BR-22451900 Gavea Rio de Janeiro RJ Brazil

This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous mathematical foundations, we impel practical usage of time consistent models as we provide practitioners with an intuitive economic interpretation for the referred recursive objective function. We also discourage time-inconsistent models by arguing that the associated policies are sub-optimal. We developed a new methodology to compute the sub-optimality gap associated with a time-inconsistent policy, providing practitioners with an objective method to quantify practical consequences of time inconsistency. Our results hold for a quite general class of problems and we choose, without loss of generality, a CVaR-based portfolio selection application to illustrate the developed concepts. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Time consistency dynamic stochastic programming Risk aversion Conditional Value-at-Risk (CVaR) Portfolio selection

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Long-term individual financial planning under stochastic dominance constraints

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ANNALS OF OPERATIONS RESEARCH 2020年第2期292卷 973-1000页

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

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 ofsecond order stochastic dominance(SSD) constraints on different specifications of a family objective function and with respect to three alternative benchmark policies. We define astochastic linear programin 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 implyfirst 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.

关键词： dynamic stochastic programming stochastic dominance Asset-liability management Goal-based investing Life cycle policy Consumption-investment trade-off

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Parallelization and aggregation of nested benders decomposition

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ANNALS OF OPERATIONS RESEARCH 1998年 81卷 163-187页

作者： Dempster, MAH Thompson, RT Univ Cambridge Judge Inst Management Studies Cambridge CB2 1AG England

dynamic multistage stochastic linear programming has many practical applications for problems whose current decisions have to be made under future uncertainty. There are a variety of methods for solving these problems including nested Benders decomposition. In this method, recently shown to be superior to the alternatives for large problems, the problem is decomposed into a set of smaller linear programming problems. These problems can be visualised as being attached to the nodes of a tree which is formed from the realizations of the random data vectors determining the uncertainty in the problem. The tree is traversed forwards and backwards, with information from the solutions to each nodal linear programming problem being passed to its immediate descendants by the formation of their right hand sides and to its immediate ancestor in the form of cuts. Problems in the same time period can be solved independently and it is this inherent parallelism that is exploited in our parallel nested Benders algorithm. A parallel version of the MSLiP nested Benders code has been developed and tested on various types of MIMD machines. The differing structures of the test problems cause differing levels of speed-up. Results show that problems with few variables and constraints per node do not gain from this parallelization. Stage aggregation has been successfully exploited for such problems to improve their parallel solution efficiency by increasing the size of the nodes and therefore the time spent calculating relative to the time spent communicating between processors.

关键词： linear programming dynamic stochastic programming nested Benders decomposition parallel algorithms aggregation MIMD computers

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A strategic decision support system framework for energy-efficient technology investments

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TOP 2017年第2期25卷 249-270页

作者： Cano, Emilio L. Moguerza, Javier M. Ermolieva, Tatiana Yermoliev, Yurii Rey Juan Carlos Univ Madrid Spain Int Inst Appl Syst Anal Vienna Austria

Energy systems optimization under uncertainty is increasing in its importance due to on-going global de-regulation of the energy sector and the setting of environmental and efficiency targets which generate new multi-agent risks requiring a model-based stakeholders dialogue and new systemic regulations. This paper develops an integrated framework for decision support systems (DSS) for the optimal planning and operation of a building infrastructure under appearing systemic de-regulations and risks. The DSS relies on a new two-stage, dynamic stochastic optimization model with moving random time horizons bounded by stopping time moments. This allows to model impacts of potential extreme events and structural changes emerging from a stakeholders dialogue, which may occur at any moment of the decision making process. The stopping time moments induce endogenous risk aversion in strategic decisions in a form of dynamic VaR-type systemic risk measures dependent on the system's structure. The DSS implementation via an algebraic modeling language (AML) provides an environment that enforces the necessary stakeholders dialogue for robust planning and operation of a building infrastructure. Such a framework allows the representation and solution of building infrastructure systems optimization problems, to be implemented at the building level to confront rising systemic economic and environmental global changes.

关键词： Decision support systems dynamic stochastic programming Uncertainty modelling Strategic and operational planning

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EVPI-based importance sampling solution procedures for multistage stochastic linear programmes on parallel MIMD architectures

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ANNALS OF OPERATIONS RESEARCH 1999年 90卷 161-184页

作者： Dempster, MAH Thompson, RT Univ Cambridge Judge Inst Management Studies Cambridge England

Multistage stochastic linear programming has many practical applications for problems whose current decisions have to be made under future uncertainty. There are a variety of methods for solving the deterministic equivalent forms of these dynamic problems, including the simplex and interior-point methods and nested Benders decomposition, which decomposes the original problem into a set of smaller linear programming problems and has recently been shown to be superior to the alternatives for large problems. The Benders subproblems can be visualised as being attached to the nodes of a tree which is formed from the realisations of the random data process determining the uncertainty in the problem. This paper describes a parallel implementation of the nested Benders algorithm which employs a farming technique to parallelize nodal subproblem solutions. Differing structures of the test problems cause differing levels of speed-up on a variety of multicomputing platforms: problems with few variables and constraints per node do not gain from this parallelisation. We therefore employ stage aggregation to such problems to improve their parallel solution efficiency by increasing the size of the nodes and therefore the time spent calculating relative to the time spent communicating between processors. A parallel version of a sequential importance sampling solution algorithm based on local expected value of perfect information (EVPI) is developed which is applicable to extremely large multistage stochastic linear programmes which either have too many data paths to solve directly or a continuous distribution of possible realisations. It utilises the parallel nested Benders algorithm and a parallel version of an algorithm designed to calculate the local EVPI values for the nodes of the tree and achieves near linear speed-up.

关键词： linear programming dynamic stochastic programming nested Benders decomposition parallel algorithms aggregation MIMD computers

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