Stochastic Yield Research Articles

Total nitrogen transformation dynamics with deterministic and stochastic yield coefficients

Total nitrogen transformation dynamics with deterministic and stochastic yield coefficients

Stochastic Analysis and Neural Network-Based Yield Prediction with Precision Agriculture

In this paper, we propose a general mathematical model for analyzing yield data. The data analyzed in this paper come from a characteristic corn field in the upper midwestern United States. We derive expressions for statistical moments from the underlying stochastic model. Consequently, we illustrate how a particular feature variable contributes to the statistical moments (and in effect, the characteristic function) of the target variable (i.e., yield). We also analyze the data with neural network techniques and provide two methods of data analysis. This mathematical model and neural network-based data analysis allow for better understanding of the variability within the data set, which is useful to farm managers attempting to make current and future decisions using the yield data. Lenders and risk management consultants may benefit from the insights of this mathematical model and neural network-based data analysis regarding yield expectations.

Pricing commodity-linked bonds with stochastic convenience yield, interest rate and counterparty credit risk: application of Mellin transform methods

Pricing commodity-linked bonds with stochastic convenience yield, interest rate and counterparty credit risk: application of Mellin transform methods

Multiobjective land–water allocation model for sustainable agriculture with predictive stochastic yield response

AbstractConsider an agricultural land–water resource allocation problem in which yields are spatial dependent and stochastically correlated. To achieve sustainability, we formulate a multiobjective (MO) optimization problem, in which the decision maker determines the cultivation areas and the supplemental irrigation water levels at different locations, with social, economic, and environmental goals in mind. For the social goal, we minimize the root mean squared difference of incomes among locations. For the economic goal, we minimize the production risk. We show that minimizing production risk is equivalent to maximizing the service level, when demand is normally distributed. For the environmental goal, we minimize the resource utilization. Assume that the yield vector at different locations follows a multivariate normal distribution. We formulate the MO optimization problem using a weight global criterion method, and we provide a sufficient condition for convex quadratic programming. We demonstrate the applicability of our proposed framework in the case study of sugarcane production in Thailand. To capture yield response to water, we propose several models including linear and nonlinear regressions, and we obtain the closed‐form expression for the linear and probit yield response models. The numerical experiment reveals that our solution significantly improves the social and economic goals, compared to the current policy. Finally, we illustrate how to apply our model to quantify the monetary value from reducing yield variability, which could be resulted from smart irrigation or precision agriculture.

A blackbox yield estimation workflow with Gaussian process regression applied to the design of electromagnetic devices

In this paper an efficient and reliable method for stochastic yield estimation is presented. Since one main challenge of uncertainty quantification is the computational feasibility, we propose a hybrid approach where most of the Monte Carlo sample points are evaluated with a surrogate model, and only a few sample points are reevaluated with the original high fidelity model. Gaussian process regression is a non-intrusive method which is used to build the surrogate model. Without many prerequisites, this gives us not only an approximation of the function value, but also an error indicator that we can use to decide whether a sample point should be reevaluated or not. For two benchmark problems, a dielectrical waveguide and a lowpass filter, the proposed methods outperform classic approaches.

Closed-form analytical solutions for options on agricultural futures with seasonality and stochastic convenience yield

Abstract Stochastic commodity price models play a significant role in the pricing and hedging of commodity derivatives and real assets. This paper proposes a commodity pricing model that extends the Ewald and Ouyang two-factor model by adding a time-varying function into the volatility term of convenience yield process to describe seasonality. The stochastic factors in the model are the spot price of the commodity is assumed to follow geometrical Brownian motion process with a stochastic drift, the instantaneous convenience yield follows a mean-reverting Ornstein-Uhlenbeck stochastic process with time-varying seasonal volatility. The model we propose is analytically tractable and allows us to derive closed-form pricing formulas for futures and options by using the Mellin transform method. In addition, we provide the experiments results to illustrate the important properties of commodity futures options with numerical table and graphs.

Stochastic yield catastrophes and robustness in self-assembly.

A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield.

Pricing Asian Options with Stochastic Convenience Yield and Jumps

We price Asian options on commodity futures contracts in the presence of stochastic convenience yield, stochastic interest rates and jumps in the commodity spot price. We obtain a closed-form solution for the case of a geometric average option without the presence of jumps, both for continuous and discrete averaging. This analytic result enables us to employ the geometric average option as suitable control variate for pricing the corresponding arithmetic average Asian option via Monte Carlo simulation. We observe a significant reduction in the size of confidence intervals in relation to plain Monte Carlo. Varying the parameters of the model, we obtain a good understanding as to how Asian option prices change accordingly in relation to a stochastic convenience yield. We then consider a variation of the model by adding stochastic jumps to the commodity spot price dynamics. By conditioning on the jump times first and then averaging over the sequences of jump times, we show that our control variate still provides a significant variance reduction, even though a closed-form solution for a geometric average Asian option in the presence of jumps is unavailable.

The valuation of options on index futures with stochastic dividend yields

This paper develops a valuation model for European options on index futures considering the stochastic nature of dividend yields. In addition, this research examines two subjects: first, whether the assumption of stochastic dividend yields is relevant; and second, the model's performance regarding the futures volatility curve. The model is calibrated using maximum likelihood estimation. The results suggest that the assumption of stochastic dividend yields has a significant influence in the valuation of options on index futures, even after considering commission costs. In addition, the model performs well in explaining the observed futures volatility curve. In this sense, the findings suggest that investment strategies based on mathematical models must consider the stochastic nature of dividend yields.

Application of Machine Learning to support production planning of a food industry in the context of waste generation under uncertainty

Food production is a complex process where uncertainty is very relevant (e.g. stochastic yield and demand, variability in raw materials and ingredients…), resulting in differences between planned production and actual output. These discrepancies have an economic cost for the company (e.g. waste disposal), as well as an environmental impact (food waste and increased carbon footprint). This research aims to develop tools based on data analytics to predict the magnitude of these discrepancies, improving enterprise profitability while, at the same time, reducing environmental impact aiding food waste management.A food company that produces liquid products based on fruits and vegetables was analyzed. Data was gathered on 1,795 batches, including the characteristics of the product (recipe, components used…) and the difference between the input and the output weight. Machine Learning (ML) algorithms were used to predict deviations in production, reducing uncertainties related to the amount of waste produced. The ML models had greater predictive capacity than a linear model with stepwise parameter selection. Then, uncertainty is included in the predictions using a normal distribution based on the residuals of the model. Furthermore, we also demonstrate that ML models can be used as a tool to identify possible production anomalies.This research shows innovative ways to deal with uncertainty in production planning using modern methods in the field of operation research. These tools improve classical methods and provide production managers with valuable information to assess the economic benefits of improved machinery or process controls. As a consequence, accurate predictive models can potentially improve the profitability of food companies, also reducing their environmental impact.

On forward and inverse uncertainty quantification for models involving hysteresis operators

Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.

European option pricing model with generalized Ornstein\u2013Uhlenbeck process under stochastic earning yield and stochastic dividend yield

This paper aims to examine and establish the models for European option pricing which include parameters of stochastic dividend yield and stochastic earning yield. We generalize the Ornstein–Uhlenbeck process and define it as generalized Ornstein–Uhlenbeck process. We have learned that the firm stocks, according to Black–Scholes–Merton structure, obey the geometric Brownian motion process. Under a stochastic earning yield, the dividend yield complies with the generalized Ornstein–Uhlenbeck process. The firm dividend randomly deviates from the earning yield flow because of the presence of stochastic components of dynamic Wiener process of generalized Ornstein–Uhlenbeck. In this study, we model the stock price with stochastic earning yield, and stochastic dividend yield to be taking account stochastic market price of risk parameter which is mean-reverting as well. We developed explicit formulae for European call option pricing calculations. From numerical simulation, we could evaluate the performance of our new model that could be compared with other notable option pricing models by using actual option price data. The outcomes prove that our new model performance is best when compared with others.

Portfolio Optimization for Assets with Stochastic Yields and Stochastic Volatility

In this paper, we consider a stochastic portfolio optimization model for investment on a risky asset with stochastic yields and stochastic volatility. The problem is formulated as a stochastic control problem, and the goal is to choose the optimal investment and consumption controls to maximize the investor’s expected total discounted utility. The Hamilton–Jacobi–Bellman equation is derived by virtue of the dynamic programming principle, which is a second-order nonlinear equation. Using the subsolution–supersolution method, we establish the existence result of the classical solution of the equation. Finally, we verify that the solution is equal to the value function and derive and verify the optimal investment and consumption controls.

A closed-form pricing formula for vulnerable European options under stochastic yield spreads and interest rates

Abstract This paper develops a three-factor valuation model of vulnerable European options incorporating stochastic yield spreads and interest rates, which extends a constant yield spread and deterministic interest rate proposed in Hull and White [12]. The dynamics of the short-term interest rate are represented implicitly by a stochastic bond price process. Therefore, the stochastic factors in the model are the spot price of the underlying asset that follows a geometrical Brownian motion process, the yield spreads and the default-free unit discount bond that are modeled by a mean-reverting Ornstein-Uhlenbeck stochastic process. Furthermore, we exploit Mellin transform techniques to derive a closed-form solution for vulnerable European options under the Black-Scholes model, which is simply computed using the standard normal cumulative distribution function so that the pricing and hedging of vulnerable European options can be computed very accurately and rapidly. Numerical experiments demonstrate how credit risk and interest rate risk affect the prices of European options.

Analytic Formulas for Futures and Options for a Linear Quadratic Jump Diffusion Model with Stochastic Convenience Yield and Seasonality: Do Fish Jump?

Analytic Formulas for Futures and Options for a Linear Quadratic Jump Diffusion Model with Stochastic Convenience Yield and Seasonality: Do Fish Jump?

Rainfall Intensity and Frequency Explain Production Basis Risk in Cumulative Rain Index Insurance

AbstractWith minimal moral hazard and adverse selection, weather index insurance promises financial resilience to farmers struck by harsh weather conditions through swift compensation at affordable premium. Despite these advantages, the very nature of indexing gives rise to production basis risk as the selected weather indexes do not sufficiently correspond to actual damages. To address this problem, we develop a stochastic yield model, built upon a stochastic soil moisture model driven by marked Poisson rainfall. Our analysis shows that even under similar temperature and rainfall amount yields can differ significantly; this was empirically supported by a 2‐year field experiment in which rain‐fed maize was grown under very similar total rainfall. Here, the year with more intense, less‐frequent rainfall produces a better yield—a rare counter evidence to most climate change projections. Through a stochastic yield model, we demonstrate the crucial roles of rainfall intensity and frequency in determining the yield. Importantly, the model allows us to compute rainfall pattern‐related basis risk inherent in cumulative rain index insurance. The model results and a case study herein clearly show that total rainfall is a poor indicator of yield, imposing unnecessary production basis risk on farmers and false‐positive payouts on insurers. Incorporating rainfall intensity and frequency in the design of rain index insurance can offer farmers better protection, while maintaining the attractive features of the weather index insurance and thus fulfilling its promise of financial resilience.

An imputation/copula-based stochastic individual tree growth model\xa0for mixed species Acadian forests: a case study using the Nova Scotia permanent sample plot network

BackgroundA novel approach to modelling individual tree growth dynamics is proposed. The approach combines multiple imputation and copula sampling to produce a stochastic individual tree growth and yield projection system.Methods The Nova Scotia, Canada permanent sample plot network is used as a case study to develop and test the modelling approach. Predictions from this model are compared to predictions from the Acadian variant of the Forest Vegetation Simulator, a widely used statistical individual tree growth and yield model.ResultsDiameter and height growth rates were predicted with error rates consistent with those produced using statistical models. Mortality and ingrowth error rates were higher than those observed for diameter and height, but also were within the bounds produced by traditional approaches for predicting these rates. Ingrowth species composition was very poorly predicted. The model was capable of reproducing a wide range of stand dynamic trajectories and in some cases reproduced trajectories that the statistical model was incapable of reproducing. ConclusionsThe model has potential to be used as a benchmarking tool for evaluating statistical and process models and may provide a mechanism to separate signal from noise and improve our ability to analyze and learn from large regional datasets that often have underlying flaws in sample design.

Capacitated disassembly scheduling under stochastic yield and demand

The disassembly process in remanufacturing has attracted increasing attention in recent years due to the high importance of environmental issues. The paper studies a capacitated single-item multi-period disassembly scheduling problem with random yields and demands in which procured, returned items (root items) are disassembled into components or parts (leaf items) to satisfy their demands in each period. The problem is formulated as a mixed integer nonlinear program (MINLP). Notably, a chance constraint is introduced to ensure that the probability of satisfying the demand is greater than a predetermined service level, and then is approximated by a second-order cone constraint. An outer approximation (OA) based solution algorithm is proposed to solve the resulting model. Furthermore, a special case that has uniformly-distributed yield and normally-distributed demand is considered given a closed-form formulation. Extensive numerical experiments demonstrate that the proposed algorithm can achieve converged optimal solutions within much less CPU time compared with the well-known solver BONMIN. Furthermore, a scheduling process of a valve producer is also conducted to demonstrate the application in practice. In the end, managerial insights are explored and future research directions are outlined.

Selecting cotton yield response function to estimate profit-maximizing potassium fertilization rates for cotton production in Tennessee

ABSTRACTRecent research has shown that stochastic yield response functions fit data better than deterministic yield response functions; however, little research exists comparing profit-maximizing fertilizer rates for upland cotton (Gossypium hirsutum L.) using stochastic and deterministic yield response functions. The objective of this research was to determine the most appropriate yield response functional form from which to determine the profit-maximizing potassium (K) rate for cotton in Tennessee. Data were used from a nine-year K fertilizer experiment in Jackson, Tennessee. Quadratic, quadratic-plus-plateau, linear response plateau, and linear response stochastic plateau response functions were estimated to determine the yield response function that best fit the data. The linear response stochastic plateau function was the most suitable yield response function for the data. The profit-maximizing K rate ranged from 65.2 to 74.3 kg K ha−1. Misspecification of the yield response function recommended over-application of K fertilizer and decreased the producer's short-term profits.

Evaluating the long-term effectiveness of crop insurance products to provide cost effective and constant cover for maize producers under stochastic yields and prices

ABSTRACTThe long-term effectiveness of crop insurance products to provide cost effective and constant cover for maize producers against a production risk under stochastic yields and prices was evaluated. Hail occurrence in low and high risk areas was considered as the production risk, with Short-term Crop Hail Insurance (SCHI) and a Contingency Policy (Self-insurance) in the Alternative Risk Transfer (ART) market as insurance options. A financial simulation model was built to simulate the cash flow of a maize enterprise and to calculate the producer’s annual margin after interest and tax. Stochastic Efficiency with Respect to a Function (SERF) was used to rank Net Present Value (NPV) of the margin after interest and tax for different scenarios of Certainty Equivalents (CE’s) and to calculate the Utility Weighted Risk Premium (UWRP) of each scenario. The model could evaluate the effectiveness of crop insurance products. The SCHI was the preferred option in Mpumalanga (high hail risk area) and ART in North West (low hail risk area) based on the cost effectiveness of the options. The ART, however, was not able to provide constant cover at all times and the long term efficiency thereof should be carefully considered before it is applied as the sole hail risk mitigation strategy.