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
2019-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
