Dear Colleagues,
I would like to let you know about my recently published article on the
universal contingent claims and multiplicative measures that might be of
interest to you:
V.A. Kholodnyi, "Universal Contingent Claims and Multiplicative Measures:
Examples and Applications", Proceedings of the ICNPA-2002, European
Conference Publications, Cambridge, United Kingdom, 2003, 259-270.
Abstract:
We present the concept of a universal contingent claim introduced by the
author in 1995. This concept provides a unified framework for the analysis
of a wide class of financial derivatives.
A universal contingent claim describes the time evolution of a contingent
payoff. In the simplest case of a European contingent claim this time
evolution is given by a family of nonnegative linear operators, the
valuation operators. For more complex contingent claims, the time evolution
that is given by the valuation operators can be interrupted by discrete or
continuous activation of external influences that are described by,
generally speaking, nonlinear operators, the activation operators. For
example, Bermudan and American contingent claims represent
discretely and continuously activated universal contingent claims
with the activation operators being the nonlinear maximum
operators.
We show that the value of a universal contingent claim is given by a
multiplicative measure introduced by the author in 1995. Roughly
speaking, a multiplicative measure is an operator-valued (in general,
an abstract measure with values in a partial monoid) function on a
semiring of sets which is multiplicative on the union of disjoint sets.
We also show that the value of a universal contingent claim is determined by
a, generally speaking, impulsive semilinear evolution equation.
Order Information:
The Proceedings of the ICNPA-2002 can be ordered at [log in to unmask]
Sincerely,
Valery Kholodnyi
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