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Chapter 3: Martingales and Stopping Times

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Masters Stochastic Processes and FInance Fichas sobre Chapter 3: Martingales and Stopping Times, creado por mho1 el 06/06/2015.
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Resumen del Recurso

Pregunta Respuesta
filtration
Image: 3ea7ba34-4ff8-4bb7-bc79-814b86bec72a (image/png)
natural filtration
Image: dfb3356a-5b8b-479f-8c2f-758794f8b130 (image/png)
adapted
Image: f034efe6-b975-4350-a356-2837893e36e4 (image/png)
Image: ada1ace2-a583-418f-8798-72370fd71197 (image/png)
blank
Martingale (discrete parameter)
Image: c1a05a9e-855f-45a3-831d-0766431b184e (image/png)
submartingale property
Image: 4f92f86d-3d82-4230-b643-83ee11dc911e (image/png)
supermartingale property
Image: 69dea648-0e16-4dad-9d70-8e40486b4949 (image/png)
previsible (filtration)
Image: b166c883-9122-43c4-83a3-7d46bcbaf393 (image/png)
martingale transform
Image: c2ed7a6e-1266-418f-be63-d5cc7725235e (image/png)
conditions for the martingale transform being a supermartingale / martingale
Image: 0be5a4c2-9678-40b0-88dc-6d8ea0b8cc90 (image/png)
Image: c948228b-7bff-48b6-8783-247a67b88015 (image/png)
Image: 8900a979-6078-475e-a63e-8e6a943fb227 (image/png)
stopping time
Image: 4f45304a-66df-4d5d-bdaf-5eb3d79ebbf0 (image/png)
these are equivalent
Image: 28f2d68d-aa13-4b6b-97fd-7fbed27695cb (image/png)
Image: 30b68a3e-aee7-469a-b0e5-287f872e778b (image/png)
Image: 7fd69e3f-f2e3-4ff2-883a-ee88025578c6 (image/png)
Image: 65b75ea2-7353-48eb-a515-42891fda5f70 (image/png)
stopped random variable stopped process
Image: 74fb58d0-002e-4435-8d9f-28c5782c5a8d (image/png)
Image: 524af51f-a8d1-4cfc-afb4-1514ad25c099 (image/png)
N.B. cannot always take the limit as n tends to infinity and conclude that
Image: 44311e30-78b6-4ed9-907b-09cb077a8d8f (image/png)
Doob's Optional Stopping Theorem
Image: 4c90d16b-9786-4d55-b04e-91d47ba85c8f (image/png)
Image: d83d5d84-86de-4f00-b7e5-f8c6bc1c7ca5 (image/png)
Image: 8004403f-afcc-49bd-b80d-96f6e598dcb5 (image/png)
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