Davi Michel Valladão

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

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.

On the solution variability reduction of Stochastic Dual Dynamic Programming applied to energy planning

In the Brazilian energy operation planning, Stochastic Dual Dynamic Programming (SDDP) determines hydrothermal planning decisions based on auto-regressive (AR) models for associated risk factors. In this work we show that using AR models to generate scenarios leads to an undesirable drawback on SDDP: the variability of the solutions increases with respect to changes in the AR initial conditions. We propose a modified version of the risk averse SDDP algorithm aimed at reducing decisions and marginal costs variability induced by the use of AR models. We show that it is possible to obtain results with less variability and with the same characteristics of the ones obtained by traditional approach. Moreover, we argue that the proposed approach is more flexible since it is not restricted to linear models as in the original SDDP algorithm.

A multistage linear stochastic programming model for optimal corporate debt management

Large corporations fund their capital and operational expenses by issuing bonds with a variety of indexations, denominations, maturities and amortization schedules. We propose a multistage linear stochastic programming model that optimizes bond issuance by minimizing the mean funding cost while keeping leverage under control and insolvency risk at an acceptable level. The funding requirements are determined by a fixed investment schedule with uncertain cash flows. Candidate bonds are described in a detailed and realistic manner. A specific scenario tree structure guarantees computational tractability even for long horizon problems. Based on a simplified example, we present a sensitivity analysis of the first stage solution and the stochastic efficient frontier of the mean-risk trade-off. A realistic exercise stresses the importance of controlling leverage. Based on the proposed model, a financial planning tool has been implemented and deployed for Brazilian oil company Petrobras.

An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets

Robust portfolio optimization models widely presented in the financial literature usually assume that asset returns lie in a parametric uncertainty set with a controlled level of conservatism expressed in terms of the variability of the uncertain parameters. In practice however, it is not clear how investors should choose the conservatism parameter to reflect their own preferences, while considering price dynamics. In this paper, we provide a new perspective on robust portfolio optimization where we impose an intuitive loss constraint for the optimal portfolio considering asset returns in a data-driven polyhedral uncertainty set. Adaptively updated in a rolling horizon scheme, the proposed model captures price dynamics, absorbing new patterns and forgetting old ones, by means of a data-driven polyhedral-based loss constraint and an optimal mixture of asset price signals. We perform a case study to illustrate that it is possible to obtain a loss-controlled portfolio with higher expected returns than chosen benchmark strategies. Considering realistic transaction costs, out-of-sample results, obtained by applying our model for each day of the historical data (2000–2015) and updating with realized returns, indicate that our robust portfolio exhibited an enhanced performance while successfully constraining possible losses.

Assessing the Cost of Time-Inconsistent Operation Policies in Hydrothermal Power Systems

The current state-of-the-art method used for medium- and long-term planning studies of hydrothermal power system operation is the stochastic dual dynamic programming (SDDP) algorithm. The computational savings provided by this method notwithstanding, it still relies on major system simplifications to achieve acceptable performances in practical applications. In contrast with its actual implementation, simplifications in the planning stage may induce time-inconsistent policies, and consequently, a suboptimality gap. In this paper, we extend the concept of time inconsistency to measure the effects of modeling simplifications in the SDDP framework for hydrothermal operation planning. Case studies involving simplifications in transmission lines modeling and in security criteria indicate that these source of time inconsistency may result in unexpected reservoir depletion and spikes in energy market spot prices.

Co-Optimization of Energy and Ancillary Services for Hydrothermal Operation Planning Under a General Security Criterion

One of the most used methods for long-term hydrothermal operation planning is the stochastic dual dynamic programming (SDDP). Using this method, the immediate and future water opportunity cost can be balanced and an economic-dispatch policy can be defined for multiple reservoirs under inflow uncertainty. In this framework, equipment outages and reserve deliverability are generally disregarded, despite their strong impact on the operative plan. However, recent advances in robust optimization have shown how to endogenously account for security criteria in scheduling models with reduced computational burden. Within this framework, reserve deliverability is ensured across the network via the co-optimization of energy and reserves (ancillary services). In this paper, we propose a new multistage model for planning hydrothermal coordination that co-optimizes the nominal energy dispatch and individual up and down reserve allocations. The main goal of this paper is to address a general

On the solution variability reduction of stochastic dual dynamic programming applied to energy planning

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Asset liability management for open pension schemes using multistage stochastic programming under Solvency-II-based regulatory constraints

security criterion, such that, for each inflow scenario, the system is capable of withstanding the loss of up to

A Linear Stochastic Programming Model for Optimal Leveraged Portfolio Selection

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On an adaptive Black–Litterman investment strategy using conditional fundamentalist information: A Brazilian case study

components, i.e., generation or transmission assets. The proposed methodology uses the column-and-constraint generation algorithm to efficiently incorporate a compound umbrella set of contingencies in the SDDP algorithm. Results for the Brazilian power system data corroborate the effectiveness of the proposed model.