On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term
-
Giorgio Fabbri
and
Salvatore Federico
Abstract
In the deterministic context a series of well established results allow to reformulate delay differential equations (DDEs) as evolution equations in infinite dimensional spaces. Several models in the theoretical economic literature have been studied using this reformulation. On the other hand, in the stochastic case only few results of this kind are available and only for specific problems.
The contribution of the present letter is to present a way to reformulate in infinite dimension a prototype controlled stochastic DDE, where the control variable appears delayed in the diffusion term. As application, we present a model for quadratic risk minimization hedging of European options with execution delay and a time-to-build model with shock.
Some comments concerning the possible employment of the dynamic programming after the reformulation in infinite dimension conclude the letter.
©2014 Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term
- A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets
- Monopoly, Social Welfare, and Multi Product Quality
- Understanding Voting Behaviour in Complex Political Systems
- Discrete Versus Continuous Time in an Endogenous Growth Model with Durable Consumption
- A Solution for General Exchange Markets with Indivisible Goods when Indifferences are Allowed
- A Perishable Inventory Model with Bonus Service for Certain Customers, Balking and N + 1 Policy
Articles in the same Issue
- Frontmatter
- On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term
- A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets
- Monopoly, Social Welfare, and Multi Product Quality
- Understanding Voting Behaviour in Complex Political Systems
- Discrete Versus Continuous Time in an Endogenous Growth Model with Durable Consumption
- A Solution for General Exchange Markets with Indivisible Goods when Indifferences are Allowed
- A Perishable Inventory Model with Bonus Service for Certain Customers, Balking and N + 1 Policy
