Testing the Local Martingale Theory of Bubbles using Cryptocurrencies

2020 ◽  
Author(s):  
Soon Hyeok Choi ◽  
Robert Jarrow
Keyword(s):  
Local Martingale ◽  
Martingale Theory

scholarly journals Local martingale and pathwise solutions for an abstract fluids model

2011 ◽  
Vol 240 (14-15) ◽  
pp. 1123-1144 ◽  
Author(s):  
Arnaud Debussche ◽  
Nathan Glatt-Holtz ◽  
Roger Temam
Keyword(s):  
Local Martingale ◽  
Pathwise Solutions

Integral equations for compound distribution functions

1996 ◽  
Vol 33 (2) ◽  
pp. 388-399 ◽  
Author(s):  
Christian Max Møller
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Building Blocks ◽  
Distribution Functions ◽  
Jump Processes ◽  
Marked Point Processes ◽  
Martingale Theory ◽  
Compound Distribution ◽  
Change Of Variable ◽  
Fixed Period

The aim of the present paper is to introduce some techniques, based on the change of variable formula for processes of finite variation, for establishing (integro) differential equations for evaluating the distribution of jump processes for a fixed period of time. This is of interest in insurance mathematics for evaluating the distribution of the total amount of claims occurred over some period of time, and attention will be given to such issues. Firstly we will study some techniques when the process has independent increments, and then a more refined martingale technique is discussed. The building blocks are delivered by the theory of marked point processes and associated martingale theory. A simple numerical example is given.

Martingales

2021 ◽  
pp. 313-343
Author(s):  
James Davidson
Keyword(s):  
Martingale Theory ◽  
Basic Properties ◽  
Martingale Inequalities ◽  
Martingale Convergence ◽  
Doob Decomposition

This chapter summarizes the essentials of sequential conditioning and martingale theory. After a review with examples of the basic properties of martingales and semi‐martingales, including the Doob decomposition, the upcrossing inequality and martingale convergence are studied and also the role of the conditional variances in establishing convergence. The important martingale inequalities of Kolmogorov, Doob, Burkholder, and Azuma are proved.

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