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In this paper, we study the option pricing problem for the conditional Asian option that appears as a recent market product, offering a cheaper and new alternative to the regular Asian option. We develop the new characteristics of short-maturity asymptotic for the prices of the conditional Asian option provided that the underlying asset follows a local volatility model. The asymptotics for out-of-the-money and at-the-money using fixed strike conditional Asian options are presented, respectively, which provide the linear approximation description of call/put option price. Moreover, the approximating solution for the corresponding variational problem under the well-known Black–Scholes model is also given. The theoretical results derived in the paper are practically relevant and numerical experiments are shown to validate the theoretical outcomes of the paper.

In this paper, we consider the Moebius measures μxn indexed by dimension n and |x| < 1 on the unit sphere Sn−1 in ℝn (n ≥ 3), and provide a precise two-sided estimate on the order of the Beckner inequality constant with exponent p ∈ [1, 2) in the three parameters. As special cases for p = 1 and p tending to 2, our results cover those in Barthe et al. [Forum Math. (submitted for publication)] for n ≥ 3 and explore an interesting phenomenon.

In this paper, we consider a generalized stochastic model associated with affine point processes based on several classical models. In particular, we study the asymptotic behavior of the process when the initial intensity is large, i.e. the intensity of arriving events observed initially is considerably larger, which appears in many real applications. For our generalized model, we establish (i) the large deviation principle; (ii) the corresponding functional law of large numbers; (iii) the corresponding central limit theorem, that reflect the fundamentals of the process asymptotic behavior. Our obtained results include existing results as special cases with a more general structure.

The Hawkes process is a self-exciting simple point process. In this paper, we study the Moderate Deviation Principle for multivariate Hawkes processes on the large time regimes.

In this paper, we study a general dynamic contagion process that includes several standard point processes as special cases. We have developed (i) the corresponding large deviation principle; (ii) the corresponding law of large numbers; (iii) the corresponding central limit theorem, all of which are critical in describing the essential of this type of processes, and are not available in current literature. The proposed model provides a broader framework in the study of contagion processes in various applications. In particular, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for the risk model with marked dynamic contagion claim arrivals as an application.

In this paper, we proved a central limit theorem and established a moderate deviation principle for a perturbed stochastic wave equation defined on $[0,T]\times \rr^3$. This equation is driven by a Gaussian noise, white in time and correlated in space. The weak convergence approach plays an important role., 20 pages. arXiv admin note: text overlap with arXiv:1509.01757

In this paper, we study the deviation probability estimate for a leveraged exchanged-traded fund (LETF). By large deviation principle, we derive explicitly the logarithmic limit of the tail probability when the price of a LETF exceeds a given reference asset, which allows us to compute the underlying leverage ratio. Then we apply our results to various existing models, including the geometric Brownian motion (GBM) model, generalized autoregressive conditional heteroskedasticity (GARCH) model, inverse GARCH model, extended Cox–Ingersoll–Ross (CIR) model, 3/2 model, as well as the Heston and 3/2 stochastic volatility models, and to present their corresponding optimal leverage ratios, respectively.

In this paper, we study the Moderate Deviation Principle for a perturbed stochastic heat equation in the whole space $\rr^d, d\ge1$. This equation is driven by a Gaussian noise, white in time and correlated in space, and the differential operator is a fractional derivative operator. The weak convergence method plays an important role., Comment: arXiv admin note: text overlap with arXiv:1401.2798, arXiv:1505.04671, arXiv:math/0610769 by other authors