17 research outputs found
On Some Optimal Stopping Problems with Constraint
We consider the optimal stopping problem of a Markov process {xt : t †0} when the controller is allowed to stop only at the arrival times of a signal, that is, at a sequence of instants {Ïn : n †1} independent of {xt : t †0}. We solve in detail this problem for general MarkovâFeller processes with compact state space when the interarrival times of the signal are independent identically distributed random variables. In addition, we discuss several extensions to other signals and to other cases of state spaces. These results generalize the works of several authors where {xt : t †0} was a diffusion process and where the signal arrives at the jump times of a Poisson process
Dynkin games with Poisson random intervention times
This paper introduces a new class of Dynkin games, where the two players are
allowed to make their stopping decisions at a sequence of exogenous Poisson
arrival times. The value function and the associated optimal stopping strategy
are characterized by the solution of a backward stochastic differential
equation. The paper further applies the model to study the optimal conversion
and calling strategies of convertible bonds, and their asymptotics when the
Poisson intensity goes to infinity
Pairs Trading: An Optimal Selling Rule with Constraints
The focus of this paper is on identifying the most effective selling strategy
for pairs trading of stocks. In pairs trading, a long position is held in one
stock while a short position is held in another. The goal is to determine the
optimal time to sell the long position and repurchase the short position in
order to close the pairs position. The paper presents an optimal pairs-trading
selling rule with trading constraints. In particular, the underlying stock
prices evolve according to a two dimensional geometric Brownian motion and the
trading permission process is given in terms of a two-state {trading allowed,
trading not allowed} Markov chain. It is shown that the optimal policy can be
determined by a threshold curve which is obtained by solving the associated HJB
equations (quasi-variational inequalities). A closed form solution is obtained.
A verification theorem is provided. Numerical experiments are also reported to
demonstrate the optimal policies and value functions
Reflected Diffusion Processes with Jumps
A stochastic differential equation of Wiener-Poisson type is considered in a d-dimensional bounded region. By using a penalization argument on the domain, we are able to prove the existence and uniqueness of solutions in the strong sense. The main assumptions are Lipschitzian coefficients, either convex or smooth domains and a regular outward reflecting direction. As a direct consequence, it is verified that the reflected diffusion process with jumps depends on the initial date in a Lipschitz fashion
On Some Ergodic Impulse Control Problems with Constraint
This paper studies the impulse control of a general Markov process under the average (or ergodic) cost when the impulse instants are restricted to be the arrival times of an exogenous process, and this restriction is referred to as a constraint. A detailed setting is described, a characterization of the optimal cost is obtained as a solution of an HJB equation, and an optimal impulse control is identified
On Optimal Stopping and Impulse Control with Constraint
The optimal stopping and impulse control problems for a Markov-Feller process are considered when the controls are allowed only when a signal arrives. This is referred to as control problems with constraint. In [28, 29, 30], the HJB equation was solved and an optimal control (for the optimal stopping problem, the discounted impulse control problem and the ergodic impulse control problem, respectively) was obtained, under suitable conditions, including a setting on a compact metric state space. In this work, we extend most of the results to the situation where the state space of the Markov process is locally compact
On Some Impulse Control Problems with Constraint
The impulse control of a MarkovâFeller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified