Some solvable stochastic control problems with delay
Reads0
Chats0
TLDR
A verification theorem of variational inequality type is proved and is applied to solve explicitly some classes of optimal harvesting delay problems.Abstract:
We consider optimal harvesting of systems described by stochastic differential equations with delay. We focus on those situations where the value function of the harvesting problem depends on the initial path of the process in a simple way, namely through its value at 0 and through some weighted averages A verification theorem of variational inequality type is proved. This is applied to solve explicitly some classes of optimal harvesting delay problemsread more
Citations
More filters
Journal ArticleDOI
A Delayed Black and Scholes Formula
TL;DR: In this article, an explicit formula for pricing European options when the underlying stock price follows nonlinear stochastic functional differential equations with fixed and variable delays is developed, and the derivation of the option-pricing formula is based on an equivalent local martingale measure.
Posted Content
A Delayed Black and Scholes Formula II
TL;DR: In this article, the authors developed an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion terms.
A maximum principle for optimal control of stochastic systems with delay, with applications to finance
Bernt Øksendal,Agnès Sulem +1 more
TL;DR: In this article, the authors consider optimal control problems for systems described by stochastic differential equations with delay and prove two (sufficient) maximum principles for certain classes of such systems.
Journal ArticleDOI
Dynamic programming in stochastic control of systems with delay
TL;DR: In this article, the authors consider optimal control problems for systems described by stochastic differential equations with delay (SDDE) and prove a version of the dynamic programming principle for a general class of such problems.
Journal ArticleDOI
Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations
TL;DR: In this article, the authors studied optimal control problems for (time-delayed) stochastic differential equations with jumps, and established sufficient and necessary stoachastic maximum principles for an optimal control of such systems.
References
More filters
Book
Stochastic integration and differential equations
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.
Book
Functional Integration And Partial Differential Equations
TL;DR: The authors discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory and provides results that have not previously appeared in book form, including research contributions of the author.
Journal ArticleDOI