# Martingales

### CONDITIONAL EXPECTATION AND MARTINGALES

CONDITIONAL EXPECTATION AND **MARTINGALES** 1. INTRODUCTION **Martingales** play a role in stochastic processes roughly similar to that played by conserved

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### Chapter5 Martingales.

160 CHAPTER5. **MARTINGALES**. Exercise 5.4. In order to establish that a nonnegative **martingale** has an almost sure limit (which may not bean L 1 limit) show that we can assume, without loss of generality, that we are in the following situation. = 1 j =1 R ; F n =[ x 1, ···,x n]; X j(

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### Martingales

**Martingales** H. Krieger, Mathematics 156, Harvey Mudd College Fall, 2008 Deﬁnitions: A sequence {X n : n = 0,1,2,...} of random variables, with

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### CONDITIONAL EXPECTATION AND MARTINGALES

{ X of integrable real (or complex) random variables with the property that for every bounded

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### LECTURES 3AND 4: MARTINGALES

LECTURES 3AND 4: **MARTINGALES** 1. Introduction In an arbitrage-free market, the share price of any traded asset at timet=0 is the expected value, under an equilibrium measure, of its discounted price at market terminationt=T.

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### MARTINGALES, DIFFUSIONS AND FINANCIAL MATHEMATICS

iv LITERATURE There are very many books on the topics of the course. The list below isa small selection. Discrete **martingales** are discussed inmost advanced introductions to general probability theory.

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### Notes on Random Variables, Expectations, Probability ...

Eco 315.2 Spring 2007 C.Sims Notes on Random Variables, Expectations, Probability Densities, and **Martingales** Includes Exercise Due Tuesday, April 4.

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### References

Mathematical Techniques in Finance, Proof of Theorem 2.11, c 2005 Aleı µ Cerný 1 Proof of Theorem 2.11 1. The "if" part. (a) De–ne the subspace of all pay-o⁄s with non-positive price,

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### MARTINGALES IN BANACH LATTICES

**MARTINGALES** IN BANACH LATTICES VLADIMIR G. TROITSKY Dedicated to the memory of Yuri Abramovich, my friend and advisor. Abstract. Inthis article we present a version ofmartingaletheoryinterms ofBanach

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### Martingales in Sequential Analysis and Time Series, 1945{1985

**Martingales** in Sequential Analysis and Time Series, 1945{1985 Tze LeungLa i y Abstract This paper reviews the history of **martingales** in sequential analysis, beginning with Wald'sground-breaking paper in 1945 that laid the foundations for the subject, and ending in the decade 1975{1985 when the ...

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