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Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations

Aditi Dandapani

Title:
Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations
Author(s):
Dandapani, Aditi
Thesis Advisor(s):
Protter, Philip E.
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Applied Physics and Applied Mathematics
Persistent URL:
Abstract:
In this thesis, we study the strict local martingale property of solutions of various types of stochastic differential equations and the effect of an initial expansion of the filtration on this property. For the models we consider, we either use existing criteria or, in the case where the stochastic differential equation has jumps, develop new criteria that can can detect the presence of the strict local martingale property. We develop deterministic sufficient conditions on the drift and diffusion coefficient of the stochastic process such that an enlargement by initial expansion of the filtration can produce a strict local martingale from a true martingale. We also develop a way of characterizing the martingale property in stochastic volatility models where the local martingale has a general diffusion coefficient.
Subject(s):
Stochastic differential equations
Martingales (Mathematics)
Mathematics
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249
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Suggested Citation:
Aditi Dandapani, , Enlargement of Filtration and the Strict Local Martingale Property in Stochastic Differential Equations, Columbia University Academic Commons, .

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