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In this paper, we study the joint Laplace transform of the sticky Brownian motion on an interval, its occupation time at zero and its integrated process. The perturbation approach of Li and Zhou [The joint Laplace transforms for diffusion occupation times, Adv. Appl. Probab.45 (2013) 1049–1067] is adopted to convert the problem into the computation of three Laplace transforms, which is essentially equivalent to solving the associated differential equations with boundary conditions. We obtain the explicit expression for the joint Laplace transform in terms of the modified Bessel function and Airy functions. [ABSTRACT FROM AUTHOR]

In this paper, we study option prices under a feasible threshold diffusion model subject to jump-to-default risk where the default intensity takes a negative power of the underlying stock price. The model incorporates the regime switches endogenously by assuming the volatility to shift from one regime to another when the stock price crosses the pre-specified threshold level. This threshold can be understood as the psychological price barrier. Using the probabilistic approach, we obtain the Laplace-transform-based analytical solutions to the pricing problem of European vanilla options. Numerical analysis in the end examines the option-related quantities using the derived results and shows the impact of jump-to-default risk and threshold effect. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some properties of the doubly skewed CIR process which is an extension of skew Brownian motion. The weak existence and pathwise uniqueness of this process is considered in the beginning. Then we present the explicit formulae for the stationary density function and show that the process is positive Harris recurrent and geometrically ergodic. We also provide the explicit Laplace transforms of the first hitting times by using the basic theory of linear diffusions. As a natural corollary, the expectations of the first hitting times are given in the end. [ABSTRACT FROM AUTHOR]