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Full-Text Articles in Physical Sciences and Mathematics
Localization And Compactness Of Operators On Fock Spaces, Zhangjian Hu, Xiaofen Lv, Brett D. Wick
Localization And Compactness Of Operators On Fock Spaces, Zhangjian Hu, Xiaofen Lv, Brett D. Wick
Mathematics Faculty Publications
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Short-Time Expansions For Call Options On Leveraged Etfs Under Exponential Lévy Models With Local Volatility, José E. Figueroa-López, Ruoting Gong, Matthew Lorig
Short-Time Expansions For Call Options On Leveraged Etfs Under Exponential Lévy Models With Local Volatility, José E. Figueroa-López, Ruoting Gong, Matthew Lorig
Mathematics Faculty Publications
In this article, we consider the small-time asymptotics of options on a leveraged exchange-traded fund (LETF) when the underlying exchange-traded fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. We show that leverage modifies the drift, volatility, jump intensity, and jump distribution of a LETF in addition to inducing the possibility of default, even when the underlying ETF price remains strictly positive. Our main results are closed-form expressions for the leading-order terms of off-the-money European call and put LETF option prices near expiration, with explicit error bounds. These results show that the price of an …
A Non-Commutative Julia Inequality, John E. Mccarthy, James E. Pascoe
A Non-Commutative Julia Inequality, John E. Mccarthy, James E. Pascoe
Mathematics Faculty Publications
We prove a Julia inequality for bounded non-commutative functions on polynomial polyhedra. We use this to deduce a Julia inequality for holomorphic functions on classical domains in Cd. We look at differentiability at a boundary point for functions that have a certain regularity there.
Commutators, Little Bmo And Weak Factorization, Xuan Thinh Duong, Ji Li, Brett D. Wick, Dongyong Yang
Commutators, Little Bmo And Weak Factorization, Xuan Thinh Duong, Ji Li, Brett D. Wick, Dongyong Yang
Mathematics Faculty Publications
In this paper, we provide a direct and constructive proof of weak factorization of h1 (ℝ×ℝ) (the predual of little BMO space bmo(ℝ×ℝ) studied by Cotlar-Sadosky and Ferguson-Sadosky), i.e., for every f Є h1 (ℝ×ℝ) there exist sequences {αkj} Є l and functions gjk, hkj Є L2 (ℝ2 ) such that [Equation Unavailable] in the sense of h1 (ℝ×ℝ), where H1 and H2 are the Hilbert transforms on the first and second variable, respectively. Moreover, the norm ║fh1║(ℝ×ℝ) is given in terms of ║gjk║ L2(ℝ2) and ║hkj║ L2(ℝ2). By duality, this directly implies a lower bound on the norm of …