Xuewei Yang | Nanjing University (original) (raw)

Papers by Xuewei Yang

Computational Economics, 2012

Reflected Brownian motion has been played an important role in economics, finance, queueing and m... more Reflected Brownian motion has been played an important role in economics, finance, queueing and many other fields. In this paper, we present the explicit spectral representation for the hitting time density of the reflected Brownian motion with two-sided barriers, and give some detailed analysis on the computational issues. Numerical analysis reveals that the spectral representation is more appealing than the method of numerical Laplace inversion. Two applications are included at the end of the paper.

In this paper, we investigate a sequential maximum likelihood estimator of the unknown drift para... more In this paper, we investigate a sequential maximum likelihood estimator of the unknown drift parameter for a class of reflected generalized Ornstein-Uhlenbeck processes driven by spectrally positive Lévy processes. In both of the cases of negative drift and positive drift, we prove that the sequential maximum likelihood estimator of the drift parameter is closed, unbiased, normally distributed and strongly consistent. Finally a numerical test is presented to illustrate the efficiency of the estimator.

Journal of Applied Probability, 2011

In this paper, we study first passage times of (reflected) Ornstein-Uhlenbeck processes over comp... more In this paper, we study first passage times of (reflected) Ornstein-Uhlenbeck processes over compound Poisson-type boundaries. In fact, we extend the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry et al. (J. Appl.

Quantitative Finance, 2010

In this article, we consider a regulated market and explore the default events. By using a so-cal... more In this article, we consider a regulated market and explore the default events. By using a so-called reflected Ornstein–Uhlenbeck process with two-sided barriers to formulate the price dynamics, we derive the expression for the conditional default probability. In the cases of a single observation and multiple observations, the conditional default probabilities are explicitly expressed in terms of the inverse Laplace

Insurance Mathematics & Economics, 2010

JEL classification: C13 C15 F31

Quantitative Finance, 2011

ABSTRACT

Journal of Statistical Planning and Inference, 2011

In this paper, we investigate the maximum likelihood estimation for the reflected Ornstein-Uhlenb... more In this paper, we investigate the maximum likelihood estimation for the reflected Ornstein-Uhlenbeck (ROU) processes based on continuous observations. Both the cases with one-sided barrier and two-sided barriers are considered. We derive the explicit formulas for the estimators, and then prove their strong consistency and asymptotic normality. Moreover, the bias and mean square errors are represented in terms of the solutions to some PDEs with homogeneous Neumann boundary conditions. We also illustrate the asymptotic behavior of the estimators through a simulation study.

In this paper, we consider a general Lévy risk model with two-sided jumps and a constant dividend... more In this paper, we consider a general Lévy risk model with two-sided jumps and a constant dividend barrier. We connect the ruin problem of the ex-dividend risk process with the first passage problem of the Lévy process reflected at its running maximum. We prove that if the positive jumps of the risk model form a compound Poisson process and the remaining part is a spectrally negative Lévy process with unbounded variation, the Laplace transform (as a function of the initial surplus) of the upward entrance time of the reflected (at the running infimum) Lévy process exhibits the smooth pasting property at the reflecting barrier. When the surplus process is described by a double exponential jump diffusion in the absence of dividend payment, we derive some explicit expressions for the Laplace transform of the ruin time, the distribution of the deficit at ruin, and the total expected discounted dividends. Numerical experiments concerning the optimal barrier strategy are performed and new empirical findings are presented.

Advances in Applied Probability, 2010

We consider a portfolio optimization problem in a defaultable market. The investor can dynamicall... more We consider a portfolio optimization problem in a defaultable market. The investor can dynamically choose a consumption rate and allocate his/her wealth among three financial securities: a defaultable perpetual bond, a default-free risky asset, and a money market account. Both the default risk premium and the default intensity of the defaultable bond are assumed to rely on some stochastic factor which is described by a diffusion process. The goal is to maximize the infinite-horizon expected discounted log utility of consumption. We apply the dynamic programming principle to deduce a Hamilton-Jacobi-Bellman equation. Then an optimal Markov control policy and the optimal value function is explicitly presented in a verification theorem. Finally, a numerical analysis is presented for illustration.