 We define a notion of isomorphism for financial markets in both discrete and continuous time. We classify complete one-period markets. We define an invariant of continuous time complete markets which we call the absolute market price of risk. This invariant plays a role analogous to the curvature in Riemannian geometry. We classify markets when this invariant takes a simple form . We show that in general markets with non-trivial automorphism groups admit mutual fund theorems and prove a number of such theorems.
Two markets should be considered isomorphic if they are financially indistinguishable. We define a notion of isomorphism for financial markets in both discrete and continuous time. We then seek to identify the distinct isomorphism classes, that is to classify markets. We classify complete one-period markets. We define an invariant of continuous time complete markets which we call the absolute market price of risk. This invariant plays a role analogous to the curvature in Riemannian geometry. We classify markets when the absolute market price of risk is deterministic . We show that , in general, markets with non-trivial automorphism groups admit mutual fund theorems . We prove a number of such theorems.
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Two markets should be considered isomorphic if they are financially indistinguishable.
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classify
then seek to identify the distinct isomorphism classes, that is to classify markets. We classify
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this invariant takes a simple form
the absolute market price of risk is deterministic
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in general
, in general,
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and
. We