Juliang Yin

It is well-known that pretesting the presence of the jump component in an underlying price process is crucial for modeling this process. In this paper, we propose a consistent test for jump intensity of the conditional Poisson process in a stochastic volatility jump diffusion model. Theoretically, we derive the infill and long-span asymptotic properties of realized power variation under some suitable conditions, and verify the asymptotic size and power of the proposed test. Furthermore, the finite-sample performance of our proposed test is illustrated through simulation analysis, and an application to real price series provides empirical evidence of significant jump intensities.

This paper considers the issue of optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market. In our model, the price process is composed of a money market account and a default-free risky asset, assuming they rely on a stochastic economic factor described by a diffusion process. A defaultable perpetual bond is depicted by the reduced-form model, and both the default risk premium and the default intensity of it rely on the stochastic economic factor. Our goal is to maximize the infinite horizon expected discounted power utility of the consumption. Applying the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations and analyze them using the so-called sub-super solution method to prove the existence and uniqueness of their classical solutions. Next, we use a verification theorem to derive the explicit formula for optimal investment and consumption strategies. Finally, we provide a sensitivity analysis.

In this study, we consider a class of high-dimensional longitudinal data with a large number of covariates, which arises frequently in the fields of bioinformatics and public health studies. In this setting, we study some asymptotic properties of the general generalized estimating equation (GEE) estimator when the dimension of covariates and the sample size reach infinity. Specifically, we establish the existence, consistency, and asymptotic normality of the GEE estimator under appropriate regularity conditions. The performance of the established theory is illustrated using Monte Carlo simulations. The main result of this study is a generalization of the results on natural link functions by considering nonnatural link functions.

Counterparty credit risk (CCR) is a significant risk factor that financial institutions have to consider in today’s context, and the COVID-19 pandemic and military conflicts worldwide have heightened concerns about potential default risk. In this work, we investigate the changes in the value of financial derivatives due to counterparty default risk, i.e., total value adjustment (XVA). We perform the XVA for multi-asset option based on the multivariate Carr–Geman–Madan–Yor (CGMY) processes, which can be applied to a wider range of financial derivatives, such as basket options, rainbow options, and index options. For the numerical methods, we use the Monte Carlo method in combination with the alternating direction implicit method (MC-ADI) and the two-dimensional Fourier cosine expansion method (MC-CC) to find the risk exposure and make value adjustments for multi-asset derivatives.

This paper is concerned with the domain stabilization in probability in a fixed time for nonlinear stochastic systems. More specifically, given a target domain , a probability and a fixed time , we aim to find suitable state feedback control laws such that the trajectory of the resulting closed‐loop system, starting from outside , will reach the target domain in the fixed time with the minimum probability . To this end, we prove a local existence and uniqueness result of solutions to nonlinear stochastic systems under mild conditions, and derive upper bounds of the mean of the first hitting time with respect to under various rigorous conditions. By these results, a Lyapunov‐based controller design is given to guarantee the domain stability for nonlinear stochastic systems with affine control inputs. Besides, inequalities of quadratic forms focusing on semi‐linear stochastic systems are used to design a linear state feedback controller for achieving the domain stability in probability. Several examples are given for demonstration.

By establishing a connection between a quantile regression and an asymmetric Laplace distribution (ALD), this paper considers the maximum likelihood estimation of parameters of a quantile autoregression model with Markovian switching (MSQAR), where the error terms obey ALD whose scale parameter depends on regime shifts. By utilizing the mixture representation of ALD, we develop an effective ML approach for estimating parameters of MSQAR models, and obtain closed-form estimators of unknown parameters via the EM algorithm. Consistency and asymptotic normality of estimators are shown by extending some techniques adopted in Douc, Moulines, and Rydén (2004). Also, we extend some asymptotic results of estimators to the case where the conditional quantile regression model is misspecified. Furthermore, the proposed approach is illustrated by simulations and empirical data. Simulation results show that the procedure performs well in finite samples, and the empirical analysis not only supports the existence of regime-switching in the quantile autoregression model, but also has a good performance on data fitting.

This paper studies an insurer's optimal investment portfolio under the mean-variance criterion. The financial market consists of a riskless bond and a risky asset, and the latter's volatility is random. We are extending the Cox–Ingersoll–Ross (CIR) model to the case with jumps, where it is modeled by a jump-diffusion stochastic differential equation (SDE). We use a Lévy SDE to describe the risk process we have, in which we extend the classic Cramér-Lundberg model to the Lévy process, and additionally introduce the stochastic volatility into this model. We assume that the insurer in question is a mean-variance optimizer. In other words, the decision that this insurer faces is to simultaneously maximize and minimize the mean and variance of his/her terminal wealth by selecting an optimal portfolio. We have uncovered closed-form solutions to the mean-variance problem with respect to the efficient strategy and efficient frontier by solving for expected utility maximization of a quadratic function through the martingale method. Finally, we give a numerical example that analyzes the economic behavior of the efficient frontier.