177,574 research outputs found
Wheat forecast economics effect study
A model to assess the value of improved information regarding the inventories, productions, exports, and imports of crop on a worldwide basis is discussed. A previously proposed model is interpreted in a stochastic control setting and the underlying assumptions of the model are revealed. In solving the stochastic optimization problem, the Markov programming approach is much more powerful and exact as compared to the dynamic programming-simulation approach of the original model. The convergence of a dual variable Markov programming algorithm is shown to be fast and efficient. A computer program for the general model of multicountry-multiperiod is developed. As an example, the case of one country-two periods is treated and the results are presented in detail. A comparison with the original model results reveals certain interesting aspects of the algorithms and the dependence of the value of information on the incremental cost function
Optimization of crude oil operations scheduling by applying a two-stage stochastic programming approach with risk management
ProducciĂłn CientĂficaThis paper focuses on the problem of crude oil operations scheduling carried out in a system composed of a refinery and a marine terminal, considering uncertainty in the arrival date of the ships that supply the crudes. To tackle this problem, we develop a two-stage stochastic mixed-integer nonlinear programming (MINLP) model based on continuous-time representation. Furthermore, we extend the proposed model to include risk management by considering the Conditional Value-at-Risk (CVaR) measure as the objective function, and we analyze the solutions obtained for different risk levels. Finally, to evaluate the solution obtained, we calculate the Expected Value of Perfect Information (EVPI) and the Value of the Stochastic Solution (VSS) to assess whether two-stage stochastic programming model offers any advantage over simpler deterministic approaches.Gobierno de España - proyects a-CIDiT (PID2021-123654OB-C31) and InCo4In (PGC 2018-099312-B-C31)Junta de Castilla y LeĂłn - EU-FEDER (CLU 2017-09, CL-EI-2021-07, UIC 233
Optimal investment under multiple defaults risk: A BSDE-decomposition approach
We study an optimal investment problem under contagion risk in a financial
model subject to multiple jumps and defaults. The global market information is
formulated as a progressive enlargement of a default-free Brownian filtration,
and the dependence of default times is modeled by a conditional density
hypothesis. In this Ito-jump process model, we give a decomposition of the
corresponding stochastic control problem into stochastic control problems in
the default-free filtration, which are determined in a backward induction. The
dynamic programming method leads to a backward recursive system of quadratic
backward stochastic differential equations (BSDEs) in Brownian filtration, and
our main result proves, under fairly general conditions, the existence and
uniqueness of a solution to this system, which characterizes explicitly the
value function and optimal strategies to the optimal investment problem. We
illustrate our solutions approach with some numerical tests emphasizing the
impact of default intensities, loss or gain at defaults and correlation between
assets. Beyond the financial problem, our decomposition approach provides a new
perspective for solving quadratic BSDEs with a finite number of jumps.Comment: Published in at http://dx.doi.org/10.1214/11-AAP829 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Investment and the Dynamic Cost of Income Uncertainty: the Case of Diminishing Expectations in Agriculture
This paper studies optimal investment and the dynamic cost of income uncertainty, applying a stochastic programming approach. The motivation is given by a case study in Finnish agriculture. Investment decision is modelled as a Markov decision process, extended to account for risk. A numerical framework for studying the dynamic uncertainty cost is presented, modifying the classical expected value of perfect information to a dynamic setting. The uncertainty cost depends on the volatility of income; e.g. with stationary income, the dynamic uncertainty cost corresponds to a dynamic option value of postponing investment. The numerical investment model also yields the optimal investment behavior of a representative farm. The model can be applied e.g. in planning investment subsidies for maintaining target investments. In the case study, the investment decision is sensitive to risk.Financial Economics,
Validating Sample Average Approximation Solutions with Negatively Dependent Batches
Sample-average approximations (SAA) are a practical means of finding
approximate solutions of stochastic programming problems involving an extremely
large (or infinite) number of scenarios. SAA can also be used to find estimates
of a lower bound on the optimal objective value of the true problem which, when
coupled with an upper bound, provides confidence intervals for the true optimal
objective value and valuable information about the quality of the approximate
solutions. Specifically, the lower bound can be estimated by solving multiple
SAA problems (each obtained using a particular sampling method) and averaging
the obtained objective values. State-of-the-art methods for lower-bound
estimation generate batches of scenarios for the SAA problems independently. In
this paper, we describe sampling methods that produce negatively dependent
batches, thus reducing the variance of the sample-averaged lower bound
estimator and increasing its usefulness in defining a confidence interval for
the optimal objective value. We provide conditions under which the new sampling
methods can reduce the variance of the lower bound estimator, and present
computational results to verify that our scheme can reduce the variance
significantly, by comparison with the traditional Latin hypercube approach
Dynamic shortest path problem with travel-time-dependent stochastic disruptions : hybrid approximate dynamic programming algorithms with a clustering approach
We consider a dynamic shortest path problem with stochastic disruptions in the network. We use both historical information and real-time information of the network for the dynamic routing decisions. We model the problem as a discrete time nite horizon Markov Decision Process (MDP). For networks with many levels of disruptions, the MDP faces the curses of dimensionality. We rst apply Approximate Dynamic Programming (ADP) algorithm with a standard value function approximation. Then, we improve the ADP algorithm by exploiting the structure of the disruption transition functions. We develop a hybrid ADP with a clustering approach using both a deterministic lookahead policy and a value function approximation. We develop a test bed of networks to evaluate the quality of the solutions. The hybrid ADP algorithm with clustering approach signicantly reduces the computational time, while stil providing good quality solutions. Keywords: Dynamic shortest path problem, Approximate Dynamic Programming, Disruption handling, Clusterin
Output analysis for approximated stochastic programs
Because of incomplete information and also for the sake of numerical tractability one mostly solves an approximated stochastic program instead of the underlying ''true'' decision problem. However, without an additional analysis, the obtained output (the optimal value and optimal solutions of the approximated stochastic program) should not be used to replace the sought solution of the ''true'' problem. Methods of output analysis have to be tailored to the structure of the problem and they should also reflect the source, character and precision of the input data. The scope of various approaches based on results of asymptotic and robust statistics, of the moment problem and on general results of parametric programming will be discussed from the point of view of their applicability and possible extensions
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