scholarly journals Jumping filtrations and martingales with finite variation

1994 ◽  
pp. 21-35 ◽  
Author(s):  
J. Jacod ◽  
A. V. Skorohod
Keyword(s):  
Finite Variation

scholarly journals Finite Variation of Fractional Lévy Processes

2011 ◽  
Vol 25 (2) ◽  
pp. 594-612 ◽  
Author(s):  
Christian Bender ◽  
Alexander Lindner ◽  
Markus Schicks
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Finite Variation

scholarly journals Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’

2012 ◽  
Vol 49 (3) ◽  
pp. 806-820
Author(s):  
Pieter C. Allaart
Keyword(s):  
Optimal Stopping ◽  
Continuous Time ◽  
Analogous Result ◽  
Stopping Time ◽  
Stable Processes ◽  
Finite Variation ◽  
Lévy Measure ◽  
One Dimensional ◽  
Stationary Increments ◽  
Reverse Relationship

Let (Xt)0 ≤ t ≤ T be a one-dimensional stochastic process with independent and stationary increments, either in discrete or continuous time. In this paper we consider the problem of stopping the process (Xt) ‘as close as possible’ to its eventual supremum MT := sup0 ≤ t ≤ TXt, when the reward for stopping at time τ ≤ T is a nonincreasing convex function of MT - Xτ. Under fairly general conditions on the process (Xt), it is shown that the optimal stopping time τ takes a trivial form: it is either optimal to stop at time 0 or at time T. For the case of a random walk, the rule τ ≡ T is optimal if the steps of the walk stochastically dominate their opposites, and the rule τ ≡ 0 is optimal if the reverse relationship holds. An analogous result is proved for Lévy processes with finite Lévy measure. The result is then extended to some processes with nonfinite Lévy measure, including stable processes, CGMY processes, and processes whose jump component is of finite variation.

scholarly journals Leakage of rank-dependent functionally generated trading strategies

2020 ◽  
Vol 16 (4) ◽  
pp. 573-591
Author(s):  
Kangjianan Xie
Keyword(s):  
Discrete Time ◽  
Generating Functions ◽  
Trading Strategy ◽  
Trading Strategies ◽  
Finite Variation ◽  
Leakage Effect

AbstractThis paper investigates the so-called leakage effect of trading strategies generated functionally from rank-dependent portfolio generating functions. This effect measures the loss in wealth of trading strategies due to renewing the portfolio constituent stocks. Theoretically, the leakage effect of a trading strategy is expressed explicitly by a finite-variation term. The computation of the leakage is different from what previous research has suggested. The method to estimate leakage in discrete time is then introduced with some practical considerations. An empirical example illustrates the leakage of the corresponding trading strategies under different constituent list sizes.

scholarly journals Multi-integrals of finite variation

2020 ◽  
Vol 13 (4) ◽  
pp. 459-468 ◽  
Author(s):  
Domenico Candeloro ◽  
Luisa Di Piazza ◽  
Kazimierz Musiał ◽  
Anna Rita Sambucini
Keyword(s):  
Finite Variation

Monotonically Controlled Mappings

2011 ◽  
Vol 63 (2) ◽  
pp. 460-480
Author(s):  
Libor Pavlíček
Keyword(s):  
Banach Spaces ◽  
Alternative Proof ◽  
Monotone Mappings ◽  
Finite Variation ◽  
Type Estimate ◽  
Distributional Derivative ◽  
Infinite Dimensional ◽  
New Class ◽  
Finite Dimensional ◽  
Fréchet Differentiability

Abstract We study classes of mappings between finite and infinite dimensional Banach spaces that are monotone and mappings which are differences of monotone mappings (DM). We prove a Radó–Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for DM mappings. This provides an alternative proof of the Fréchet differentiability a.e. of DM mappings. We establish a Morrey-type estimate for the distributional derivative of monotone mappings. We prove that a locally DM mapping between finite dimensional spaces is also globally DM. We introduce and study a new class of the so-called UDM mappings between Banach spaces, which generalizes the concept of curves of finite variation.

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