Tagged Questions
10
votes
1answer
200 views
Motivation of Feynman-Kac formula and its relation to Kolmogorov backward/forward equations?
Kolmogorov backward/forward equations are pdes, derived for the semigroups constructed from the Markov transition kernels.
Feynman-Kac formula is also a pde corresponding to a stochastic process ...
4
votes
1answer
141 views
Brownian Motion Covariance: max instead of min
It is known that $\operatorname{Cov}(B_t,B_s)=\min(t,s)$ where $B$ is Brownian motion.
Can one think of an Ito process or integral (preferrably plain Gaussian process) $W$ such that ...
4
votes
0answers
147 views
Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?
The following is the definition of infinitesimal generator from Oksendal.
Let $\{X_t,t\in[0,T]\}$ be a time-homogeneous It\^o diffusion in $\mathbb{R}^d$. The $\textit{infinitesimal generator}$ ...
0
votes
0answers
16 views
Boundedness of a payoff
How can i establish the the following arithmetic average payoff function is bounded?
$dS=μSdt+σSdB$
$F(x)=[(1/n)∑x(t\{i\})-K]⁺$
