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Unformatted text preview: + b b + 2 p X ( t ) dP ( t ) , where E[ P ( t )] = t and X (0) = x > 0, with probability one, while , a and b are real constants. ( Hint: Find a power transformation to convert the SDE to a constant coecient SDE. ) 4. For Jump-Diusion SDE, Find Coecients Transformable to Constant Co-ecient SDE. Show that the (It o) jump-diusion SDE for X ( t ), dX ( t ) = f ( X ( t )) dt + bX a ( t ) dW ( t ) + h ( X ( t )) dP ( t ) , (3) can be transformed by Y ( t ) = F ( X ( t )) to a constant coecient SDE , where b and a 6 = 1 are real constants, and X (0) = x > 0, with probability one. In a proper answer, derive the power forms of f ( X ( t )) and h ( X ( t )) from the constant coecient SDE conditions. Also, what is the answer when a = 1? 1...
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- Fall '09