Exact Monte Carlo likelihood-based inference for jump-diffusion processes
本文首次提出一套无需时间离散化的精确似然推断方法，用于处理离散观测的有限活动跳跃扩散过程，仅涉及蒙特卡洛误差和算法收敛误差，并通过模拟和实际案例展示了频率学派和贝叶斯两种途径。
Abstract Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus, existing approaches invariably resort to time-discretisations which inevitably lead to approximations in inference. In this paper, we give the first general collection of methodologies for exact (in this context meaning discretisation-free) likelihood-based inference for discretely observed finite activity jump-diffusions. The only sources of error involved are Monte Carlo error and convergence of expectation maximisation (EM) or Markov chain Monte Carlo (MCMC) algorithms. We shall introduce both frequentist and Bayesian approaches, illustrating the methodology through simulated and real examples.