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Stochastic Differential Equations

Definition

(A) Ring Generated by R

Definition

(Ɛ) Simple Predicable Processes

Definition

(P) Predictable σ-algebra

Definition

(R) Set of Predictable Rectangles

Definition

(Λ) Set of Predictable Locally Integrable Processes

Definition

Admissible

Definition

Asian Call Option

Theorem

Bichteler-Dellacherie Theorem

Theorem

Cross Variation

Theorem

Density of Ɛ

Definition

Derivative

Definition

Doléans Measure

Definition

European Call Option

Definition

European Put Option

Definition

Forward Contract

Theorem

Independence of Bounded RV

Definition

Itô Isometry

Theorem

Itô Isometry v2

Theorem

Itô Isometry v3

Theorem

Itô Representation Theorem

Definition

Itô Stochastic Integral

Theorem

Itô Stochastic Integral is a Local Martingale

Theorem

Itô Stochastic Integral on Ɛ is a R.C. Martingale

Theorem

Itô Stochastic Integral on Λ is a R.C. Martingale

Theorem

Itô's Formula

Theorem

Left Continuous Adapted = Predictable

Definition

Market Model

Theorem

Multidimensional Itô Formula

Definition

Mutual Variation

Theorem

Mutual Variation of Itô Stochastic Integrals

Theorem

No Arbitrage

Definition

Portfolio

Theorem

Predictable Stochastic Intervals

Theorem

Quadratic Variation

Theorem

Quadratic Variation is CAII

Definition

Replicating Portfolio

Definition

Self-Financing

Definition

Semimartingale

Definition

Semimartingale Integral

Theorem

Semimartingale Properties

Theorem

Solution to SDE

Definition

Stochastic Interval

Theorem

Stopping Time Integral