We present an approximate stochastic dynamic programming methodology for a real-world hydropower management problem, in which water must be released from reservoirs to produce electricity to power aluminum smelters ov...
详细信息
We present an approximate stochastic dynamic programming methodology for a real-world hydropower management problem, in which water must be released from reservoirs to produce electricity to power aluminum smelters over a planning horizon of a year (three-day time step). In each period, decisions are constrained by limits on the releases and the level of the four reservoirs, among others. The approach is a revisit of our previous work on simplicial approximate stochastic dynamic programming, in which the so-called cost-to-go or value functions are approximated over grid points chosen as vertices of simplices. The latter are constructed by first partitioning the reservoir level space into simplices and then iteratively subdividing existing simplices until a desired approximation error or a fixed number of grid points is reached. For each simplex, the approximation error is given by the difference between an upper and a lower bound. This scheme requires storing the list of created simplices in memory. In each iteration, the list is searched to find the existing simplex with the highest approximation error. This may be time-consuming as the number of existing simplices may be very large. In the new proposal, we avoid creating a long list of simplices by combining the original simplicial scheme with Monte Carlo simulation, similar to an exploration strategy in reinforcement learning. We benchmark the new method against its ancestor and an internal software package developed and used by an industrial partner, based on operational metrics and the concept of super-efficiency in data envelopment analysis. The Monte Carlo simplex-based scheme (the new method) outperforms the former method on all metrics considered. In addition, we compare the computational efficiency of both methods for different grid sizes. The average CPU time (over 15 replications) of the Monte Carlo simplicial approach varies between 78% and 98% of that of the simplicial method. As the grid sizes increas
Australia has a compulsory defined contribution retirement provision system, whereby employers must con-tribute a proportion of the pre-tax salary of their employees towards an individual account which cannot be acces...
详细信息
ISBN:
(纸本)9780987214355
Australia has a compulsory defined contribution retirement provision system, whereby employers must con-tribute a proportion of the pre-tax salary of their employees towards an individual account which cannot be accessed until retirement except in extraordinary circumstances. These funds are generally invested in a port-folio of financial assets from which the retiree may draw throughout retirement. Retirees under this system face two key problems when making investment and withdrawal decisions regarding this portfolio. Firstly, retirees must manage their superannuation investment portfolio to maximise their risk-adjusted returns and thereby best financially provide for their own retirement. Secondly, retirees must optimise their withdrawal pattern from the superannuation account throughout retirement so as to maximise their post-retirement lifetime utility given the need to minimise the risk of portfolio ruin prior to death. We model this issue as a dynamicstochastic optimisation problem with constraints. The market value of the portfolio is a function of the annual contributions invested by the individual throughout their career and the returns derived from their investment in uncertain financial markets. The post-retirement lifetime utility function is a function of discounted annual income throughout retirement and is therefore subject to market and inflation risk. We model the financial market uncertainties as correlated stochastic processes as projected by a variant on the Wilkie stochastic investment model developed within CSIRO, the SUPA (Simulation of Uncertainty for Pension Analysis) model. We also define an income protection asset (an inflation index linked annuity) which is available to the individual as a tool to hedge inflation risk. We then solve the dynamic super-annuation/pension portfolio optimisation problem using a numerical approach that is based on the stochastic control algorithm to calculate the conditional value functions of investors for a
To achieve good crop yields, farmers are aware of the importance of good rainfall during the growing season. However, their choice of crop to plant may not necessarily be the optimal choice when climate uncertainty ex...
详细信息
ISBN:
(纸本)9780987214355
To achieve good crop yields, farmers are aware of the importance of good rainfall during the growing season. However, their choice of crop to plant may not necessarily be the optimal choice when climate uncertainty exists. Indeed, current cropping allocations may be driven more by historical trends and tradition than by the future forecasts of climate scenarios and commodity prices. In a digital agricultural future, farmers may instead use information on crop yields and water usage to make cropping decisions each year that optimize their cash flow under the uncertainty of climate conditions and commodity prices. In this paper, we apply dynamic portfolio optimization techniques to the development of a simulation-based numerical method for making dynamic optimal cropping decisions. This method relies on a backwards recursive approach developed to solve the American option pricing problem. At each time step backwards from the end of the decision time period, the optimal expected future cash flow, or the so-called continuation function, is determined by using the Least Squares Monte Carlo method. As an example, we use a representative farm in Australia with four paddocks that can grow wheat, rice, barley and canola, and we also regard the corresponding commodity prices as stochastic variables. We compute the optimal crop rotations each year under different rainfall scenarios that maximise the expected utility over a fixed time period of 20 years. We evaluate the performance of the dynamic cropping strategies by comparing the expected value and standard deviation of future cash flows against those generated from static cropping strategies.
In the continuous fight against Bellman's Curse of Dimensionality, this work presents the first steps towards learning the Optimal Operation Policy of the electricity generation system of Uruguay, Brazil, Paraguay...
详细信息
ISBN:
(纸本)9798350346053
In the continuous fight against Bellman's Curse of Dimensionality, this work presents the first steps towards learning the Optimal Operation Policy of the electricity generation system of Uruguay, Brazil, Paraguay and Argentina with the infrastructures projected for the year 2030. The Operation Policy under consideration involves 76 state variables: one associated to the surface temperature anomaly of the Pacific Ocean in the N34 area, and 75 related to the hydroelectric reservoirs. The proposed methodology includes the design and training of two alternate neural network architectures combined with modern techniques devised for variance reduction and exploration, which were key to the success achieved.
暂无评论