Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA problem of optimal switching and singular control with discretionary stopping in portfolio selection
64
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We transform the problem into a dual two-person zero-sum game, which involves a controller, who is a minimizer and chooses a non-increasing process, and a stopper, who is a maximizer and chooses a stopping time. We derive the Hamilton-Jacobi- Bellman quasi-variational inequality(HJBQV) of a max-min type arising from the game. We provide a solution to the HJBQV and verification that it is the value of the game. We establish a duality result which allows to derive the optimal strategies and value function of the primal problem from those of the dual problem.
rate research
Read More
In this paper we study a Markovian two-dimensional bounded-variation stochastic control problem whose state process consists of a diffusive mean-reverting component and of a purely controlled one. The main problems characteristic lies in the interaction of the two components of the state process: the mean-reversion level of the diffusive component is an affine function of the current value of the purely controlled one. By relying on a combination of techniques from viscosity theory and free-boundary analysis, we provide the structure of the value function and we show that it satisfies a second-order smooth-fit principle. Such a regularity is then exploited in order to determine a system of functional equations solved by the two monotone continuous curves (free boundaries) that split the control problems state space in three connected regions. Further properties of the free boundaries are also obtained.
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, to figure out a managers decision. We formulate our model to a free boundary problem of a fully textit{nonlinear} equation. By means of a dual transformation, however, we can convert the above problem to a new free boundary problem of a textit{linear} equation. Finally, using the corresponding inverse dual transformation, we apply the theoretical results established for the new free boundary problem to obtain the properties of the optimal strategy and the optimal stopping time to achieve a certain level for the original problem over a finite time investment horizon.
We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where the objective is to maximize equity while meeting a prescribed debt/equity requirement. We take the real situation with cross impact among different assets into consideration. The resulting problem is, however, a non-convex quadratic program with a quadratic constraint and a box constraint, which is known to be NP-hard. In this paper, we first develop a successive convex optimization (SCO) approach for solving the OPD problem and show that the SCO algorithm converges to a KKT point of its transformed problem. Second, we propose an effective global algorithm for the OPD problem, which integrates the SCO method, simple convex relaxation and a branch-and-bound framework, to identify a global optimal solution to the OPD problem within a pre-specified $epsilon$-tolerance. We establish the global convergence of our algorithm and estimate its complexity. We also conduct numerical experiments to demonstrate the effectiveness of our proposed algorithms with both the real data and the randomly generated medium- and large-scale OPD problem instances.
A class of infinite horizon optimal control problems involving mixed quasi-norms of $L^p$-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization.
The problem of controlling multi-agent systems under different models of information sharing among agents has received significant attention in the recent literature. In this paper, we consider a setup where rather than committing to a fixed information sharing protocol (e.g. periodic sharing or no sharing etc), agents can dynamically decide at each time step whether to share information with each other and incur the resulting communication cost. This setup requires a joint design of agents communication and control strategies in order to optimize the trade-off between communication costs and control objective. We first show that agents can ignore a big part of their private information without compromising the system performance. We then provide a common information approach based solution for the strategy optimization problem. This approach relies on constructing a fictitious POMDP whose solution (obtained via a dynamic program) characterizes the optimal strategies for the agents. We also show that our solution can be easily modified to incorporate constraints on when and how frequently agents can communicate.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
