Semigroup theory applied to options
2002 ◽
Vol 2
(3)
◽
pp. 131-139
◽
Keyword(s):
Black and Scholes (1973) proved that under certain assumptions about the market place, the value of a European option, as a function of the current value of the underlying asset and time, verifies a Cauchy problem. We give new conditions for the existence and uniqueness of the value of a European option by using semigroup theory. For this, we choose a suitable space that verifies some conditions, what allows us that the operator that appears in the Cauchy problem is the infinitesimal generator of aC0-semigroupT(t). Then we are able to guarantee the existence and uniqueness of the value of a European option and we also achieve an explicit expression of that value.
2005 ◽
Vol 15
(08)
◽
pp. 1169-1180
◽
2015 ◽
Vol 39
(11)
◽
pp. 3116-3135
◽
2020 ◽
Vol 60
(4)
◽
pp. 663-672
2012 ◽
Vol 204-208
◽
pp. 4429-4432