53 citations · 81 across the 9 of their papers we have counts for
7 papers · 1 filter
Kolmogorov's Equations for Jump Markov Processes and their Applications to Control Problems
Eugene A. Feinberg, Albert N. Shiryaev
This paper describes the structure of solutions to Kolmogorov's equations for nonhomogeneous jump Markov processes and applications of these results to control of jump stochastic s…
Kolmogorov's Equations for Jump Markov Processes with Unbounded Jump Rates
Eugene A. Feinberg, Manasa Mandava, Albert N. Shiryaev
As well-known, transition probabilities of jump Markov processes satisfy Kolmogorov's backward and forward equations. In the seminal 1940 paper, William Feller investigated solutio…
A quickest detection problem with an observation cost
Robert C. Dalang, Albert N. Shiryaev
In the classical quickest detection problem, one must detect as quickly as possible when a Brownian motion without drift "changes" into a Brownian motion with positive drift. The c…
On solutions of Kolmogorov's equations for jump Markov processes
Eugene A. Feinberg, Manasa Mandava, Albert N. Shiryaev
This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solu…
On the one-sided Tanaka equation with drift
Ioannis Karatzas, Albert N. Shiryaev, Mykhaylo Shkolnikov
We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift λ. We observe a dichotomy in terms of the values of…
Esscher transform and the duality principle for multidimensional semimartingales
Ernst Eberlein, Antonis Papapantoleon, Albert N. Shiryaev
The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem…