相关论文: Optimal stopping for dynamic risk measures with ju…
In this paper, a characterization of the solution of impulse control problems in terms of superharmonic functions is given. In a general Markovian framework, the value function of the impulse control problem is shown to be the minimal…
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic…
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that…
We investigate the optimal reinsurance problem in a risk model with jump clustering features. This modeling framework is inspired by the concept initially proposed in Dassios and Zhao (2011), combining Hawkes and Cox processes with shot…
The aim of this paper is to investigate risk-averse and distributionally robust modeling of Stochastic Optimal Control (SOC) and Markov Decision Process (MDP). We discuss construction of conditional nested risk functionals, a particular…
We explore properties of the value function and existence of optimal stopping times for functionals with discontinuities related to the boundary of an open (possibly unbounded) set $\mathcal{O}$. The stopping horizon is either random, equal…
In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and…
In the Maslov idempotent probability calculus, expectations of random variables are defined so as to be linear with respect to max-plus addition and scalar multiplication. This paper considers control problems in which the objective is to…
This paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…
In this paper, we consider a stochastic decision problem for a system governed by a stochastic differential equation, in which an optimal decision is made in such a way to minimize a vector-valued accumulated cost over a finite-time horizon…
In this paper, we consider a risk-based optimal investment problem of an insurer in a regime-switching jump diffusion model with noisy memory. Using the model uncertainty modeling, we formulate the investment problem as a zero-sum,…
We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell…
We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (inspired by traffic models). We adapt the results in [H. M.…