In this paper we solve the problem of the existence and strong continuity of the semigroup associated with the initial value problem for a generalized Cox-Ingersoll-Ross equation for the price of a zero-coupon bond (see cite{GGMR}), on spaces of continuous functions on $[0, infty)$ which can grow at infinity. We focus on the Banach spaces $$ Y_{s} = left{fin C[0,infty): df{f(x)}{1+x^{s}}in C_0[0,infty) ight},qquad sge 1, $$ which contain the nonzero constants very common as initial data in the Cauchy problems coming from financial models. In addition, a Feynman-Kac type formula is given.

A generalized Cox-Ingersoll-Ross equation with growing initial conditions

Giséle Ruiz Goldstein;Jerome A. Goldstein;Rosamaria Mininni;Silvia Romanelli
2019

Abstract

In this paper we solve the problem of the existence and strong continuity of the semigroup associated with the initial value problem for a generalized Cox-Ingersoll-Ross equation for the price of a zero-coupon bond (see cite{GGMR}), on spaces of continuous functions on $[0, infty)$ which can grow at infinity. We focus on the Banach spaces $$ Y_{s} = left{fin C[0,infty): df{f(x)}{1+x^{s}}in C_0[0,infty) ight},qquad sge 1, $$ which contain the nonzero constants very common as initial data in the Cauchy problems coming from financial models. In addition, a Feynman-Kac type formula is given.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/254506
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