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This paper considers a newly delayed reinsurance and investment optimization problem incorporating random risk aversion, in which an insurer pursues maximization of the expected certainty equivalent of her/his terminal wealth and the…
The Helmholtz conditions are necessary and sufficient conditions for a system of second order differential equations to be variational, that is, equivalent to a system of Euler-Lagrange equations for a regular Lagrangian. On the other hand,…
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition…
In this paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting. This gives rise to time-inconsistency of the decision-maker. If the decision-maker at time t=0 can commit his/her…
In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead…
Standard formulations of prescribed worst-case disturbance energy-gain control policies for linear time-varying systems depend on all forward model data. In discrete time, this dependence arises through a backward Riccati recursion. This…
We consider in this paper, mixed relaxed-singular stochastic control problems, where the control variable has two components, the first being measure-valued and the second singular. The control domain is not necessarily convex and the…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
This paper is concerned with the uniqueness issue of open-loop equilibrium investment strategies of dynamic mean-variance portfolio selection problems with random coefficients. A unified method is developed to treat both the problems with…