اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInterbank lending with benchmark rates: Pareto optima for a class of singular control games
243
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We analyze a class of stochastic differential games of singular control, motivated by the study of a dynamic model of interbank lending with benchmark rates. We describe Pareto optima for this game and show how they may be achieved through the intervention of a regulator, whose policy is a solution to a singular stochastic control problem. Pareto optima are characterized in terms of the solutions to a new class of Skorokhod problems with piecewise-continuous free boundary. Pareto optimal policies are shown to correspond to the enforcement of endogenous bounds on interbank lending rates. Analytical comparison between Pareto optima and Nash equilibria provides insight into the impact of regulatory intervention on the stability of interbank rates.
قيم البحث
اقرأ أيضاً
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: 1. poly
nomial-time algorithms to exactly determine the number of Pareto optima and Pareto strategies; 2. a polynomial-space polynomial-delay prescribed-order enumeration algorithm for arbitrary projections of the Pareto set; 3. an algorithm to minimize the distance of a Pareto optimum from a prescribed comparison point with respect to arbitrary polyhedral norms; 4. a fully polynomial-time approximation scheme for the problem of minimizing the distance of a Pareto optimum from a prescribed comparison point with respect to the Euclidean norm.
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional s
pace X, it takes values in the positive cone of X, and it has right-continuous and nondecreasing paths. We first provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process. We then exploit the concave structure of our problem and derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we find an explicit expression of the optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained BSDE, wit
h dynamics associated to a non singular underlying forward process. Due to the non$-$Markovian environment, our main argumentation relies on the use of comparison arguments for path dependent PDEs. Our representation allows in particular to quantify the regularity of the solution to the singular stochastic control problem in terms of the space and time initial data. Our framework also extends to the consideration of degenerate diffusions, leading to the representation of the solution as the infimum of solutions to $Z-$constrained BSDEs. As an application, we study the utility maximisation problem with transaction costs for non$-$Markovian dynamics.
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 interact
ion 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.
We address the problem of multiple local optima commonly arising in optimization problems for multi-agent systems, where objective functions are nonlinear and nonconvex. For the class of coverage control problems, we propose a systematic approach for
escaping a local optimum, rather than randomly perturbing controllable variables away from it. We show that the objective function for these problems can be decomposed to facilitate the evaluation of the local partial derivative of each node in the system and to provide insights into its structure. This structure is exploited by defining boosting functions applied to the aforementioned local partial derivative at an equilibrium point where its value is zero so as to transform it in a way that induces nodes to explore poorly covered areas of the mission space until a new equilibrium point is reached. The proposed boosting process ensures that, at its conclusion, the objective function is no worse than its pre-boosting value. However, the global optima cannot be guaranteed. We define three families of boosting functions with different properties and provide simulation results illustrating how this approach improves the solutions obtained for this class of distributed optimization problems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
