A Limit Theorem on Maximum Value of Hedging with a Homogeneous Filtered Value Measure
Vol. 17 (2010), No. 4, Page 359--386.
Umezawa, Yuji
A Limit Theorem on Maximum Value of Hedging with a Homogeneous Filtered Value Measure
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Abstract:
We study a hedging problem for an European contingent claim in a certain incomplete market model by using a homogeneous filtered value measure. We consider the minimal hedging risk in discrete time model and its continuous limit. As a result, we show that this limit is described by the unique viscosity solution of a kind of Hamilton-Jacobi-Bellman equation.
Keywords: The Cauchy problem, diffusion equations with absorption, initial Dirac mass, very singular solutions, existence, nonexistence, bifurcations, branching.
Mathematics Subject Classification (2010): Primary 91B30, Secondary 60F99, 91B24.
Received: 2010-03-02
