Quantitative Fourth Moment Theorem of Functions on the Markov Triple and Orthogonal Polynomials

In this paper, we consider a quantitative fourth moment theorem for functions (random variables) defined on the Markov triple E , μ , Γ , where μ is a probability measure and Γ is the carré du champ operator. A new technique is developed to derive the fourth moment bound in a normal approximation on the random variable of a general Markov diffusion generator, not necessarily belonging to a fixed eigenspace, while previous works deal with only random variables to belong to a fixed eigenspace. As this technique will be applied to the works studied by Bourguin et al. (2019), we obtain the new result in the case where the chaos grade of an eigenfunction of Markov diffusion generator is greater than two. Also, we introduce the chaos grade of a new notion, called the lower chaos grade, to find a better estimate than the previous one.

Asset price bubbles: Invariance theorems

<p style='text-indent:20px;'>This paper provides invariance theorems that facilitate testing for the existence of an asset price bubble in a market where the price evolves as a Markov diffusion process. The test involves only the properties of the price process' quadratic variation under the statistical probability. It does not require an estimate of either the equivalent local martingale measure or the asset's drift. To augment its use, a new family of stochastic volatility price processes is also provided where the processes' strict local martingale behavior can be characterized.</p>

Application of the Fokker-Planck Kolmogorov equation to determining the mean value of nucleons generated by the direct ejection process

The statistical description of the process of direct nucleon ejection is the subject of this paper. This description is based on the generalized Fokker-Planck-Kolmogorov equation. The basic proposal is this: deterministic equations and their solutions have the mean values of the stochastic model of the ablation problem. The problem of deformation of the phase transition front is considered. The study is carried out by using the introduced stability position for the dispersion of solutions for mean values. The result of the study is the conclusion that the influence of the Markov diffusion coefficient leads to distortion of the original shape of the boundary phase transition front. The effect of the initial aspiration to resist changing the shape of the phase transition front was found.

Sharp Analytical Lower Bounds for the Price of a Convertible Bond

Analytical approximations for the price of a convertible bond within defaultable Markov diffusion models are derived in this article. Because convertible bond pricing requires time-consuming finite difference or tree pricing methods in general, such proxy formulas can help to calibrate model parameters more efficiently. The derivation is based on the idea of “Europeanizing” the American conversion option of the holder. Hence, the quality of the approximations stands and falls with the value of the early conversion premium. In practice, the latter is typically close to zero, which implies that the analytical lower bounds are incredibly sharp.