Search

In this paper, for d ≥ 1 and s ∈ (0 , d 2) , we study the Bianchi–Egnell quotient Q (f) = inf f ∈ H ˙ s (R d) \ B ‖ (- Δ) s / 2 f ‖ L 2 (R d) 2 - S d , s ‖ f ‖ L 2 d d - 2 s (R d) 2 dist H ˙ s (R d) (f , B) 2 , f ∈ H ˙ s (R d) \ B , where S d , s is the best Sobolev constant and B is the manifold of Sobolev optimizers. By a fine asymptotic analysis, we prove that when d = 1 , there is a neighborhood of B on which the quotient Q (f) is larger than the lowest value attainable by sequences converging to B . This behavior is surprising because it is contrary to the situation in dimension d ≥ 2 described recently in König (Bull Lond Math Soc 55(4):2070–2075, 2023). This leads us to conjecture that for d = 1 , Q (f) has no minimizer on H ˙ s (R d) \ B , which again would be contrary to the situation in d ≥ 2 . As a complement of the above, we study a family of test functions which interpolates between one and two Talenti bubbles, for every d ≥ 1 . For d ≥ 2 , this family yields an alternative proof of the main result of König (Bull Lond Math Soc 55(4):2070–2075, 2023). For d = 1 we make some numerical observations which support the conjecture stated above. [ABSTRACT FROM AUTHOR]

In this paper, in order to serve credit risk management, we introduce a pricing model for a vulnerable Bull Spread options in a Mixed Modified Fractional Hull-White-Vasicek stochastic volatility and stochastic interest rate model. We use Milstein scheme to find the sample paths of asset price and its volatility, and the sample paths of interest rates of asset price movement. We use the double Mellin transform to obtain an analytical vulnerable bull spread call option formula and an analytical vulnerable bull spread put option formula under fractional stochastic volatility and fractional stochastic interest rates. [ABSTRACT FROM AUTHOR]

The online version of the original article can be found at https://doi.org/10.3758/s13423-022-02238-2Correction to: Psychon Bull Revhttps://doi.org/10.3758/s13423-022-02238-2Joaquín Macedo-Pascual · Almudena Capilla · Pablo Campo3 · José Antonio Hinojosa1,4,5 · Claudia PochThis paper has been updated with open access.Publisher's noteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.By Joaquín Macedo-Pascual; Almudena Capilla; Pablo Campo; José Antonio Hinojosa and Claudia PochReported by Author; Author; Author; Author; Author [Extracted from the article]