Abstract
We show that the second order operator characterizing no-arbitrage pricing problems generates an Analytic Semigroup and therefore the Cauchy problem defining the no-arbitrage price of contingent claim contracts admits a solution. The conditions established in this paper are quite general, they encompass the sets of sufficient conditions already established in the literature. With this approach we are also able to give estimates to the derivatives of the no-arbitrage price.
This work has been partially supported by CNR, progetto strategico “Modelli e metodi per la matematica e l’ingegneria”.
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Barucci, E., Gozzi, F., Vespri, V. (1999). On a Semigroup Approach to No-arbitrage Pricing Theory. In: Dalang, R.C., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 45. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8681-9_1
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DOI: https://doi.org/10.1007/978-3-0348-8681-9_1
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