In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the...In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario simulation.However,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz setting.We provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully recovered.Numerical experiments are carried out to verify the theoretical findings.展开更多
Warranty claims forecasting plays an increasingly important role not only for preparing financial plans but also for optimizing warranty policy and improving after-sale services.In the case of new products,an importan...Warranty claims forecasting plays an increasingly important role not only for preparing financial plans but also for optimizing warranty policy and improving after-sale services.In the case of new products,an important feature is that the new generation of products often has a close connection with the previous generations of products it replaces.Thus,the warranty claims data of the previous generations of products can be used for extracting reliability information of new products.In this context,we propose a warranty claims forecasting model considering usage rate for new products sold with a two-dimensional warranty.The accelerate failure time model is introduced to investigate the effect of usage rate on product degradation.The non-homogeneous Poisson process is used to model failure counts of repairable products and the constrained maximum likelihood estimation method is used to estimate model parameters.The results of data experiments based on both simulation and real data collected from an automobile manufacturer in China show that the proposed model considering the varying usage rate outperforms the traditional models in forecasting the number of warranty claims.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11901565,12071261,11831010,11871068)by the Science Challenge Project(No.TZ2018001)by National Key R&D Plan of China(Grant No.2018YFA0703900).
文摘In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario simulation.However,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz setting.We provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully recovered.Numerical experiments are carried out to verify the theoretical findings.
基金supported by National Natural Science Foundation of China under Grant Nos.71802145,71902180,71872123,and 71801064,71532008.
文摘Warranty claims forecasting plays an increasingly important role not only for preparing financial plans but also for optimizing warranty policy and improving after-sale services.In the case of new products,an important feature is that the new generation of products often has a close connection with the previous generations of products it replaces.Thus,the warranty claims data of the previous generations of products can be used for extracting reliability information of new products.In this context,we propose a warranty claims forecasting model considering usage rate for new products sold with a two-dimensional warranty.The accelerate failure time model is introduced to investigate the effect of usage rate on product degradation.The non-homogeneous Poisson process is used to model failure counts of repairable products and the constrained maximum likelihood estimation method is used to estimate model parameters.The results of data experiments based on both simulation and real data collected from an automobile manufacturer in China show that the proposed model considering the varying usage rate outperforms the traditional models in forecasting the number of warranty claims.
