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We show the existence and uniqueness of a continuous viscosity solution of a system of partial differential equations (PDEs for short) without assuming the usual monotonicity conditions on the driver function as in Hamad\`ene and Morlais's…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems, and allow notably some coefficients to be stochastic. Our method is…
This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying…
This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity…
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…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual…
We consider Markov decision processes where the state of the chain is only given at chosen observation times and of a cost. Optimal strategies involve the optimisation of observation times as well as the subsequent action values. We…
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 consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…
In this paper, we consider the optimal dividend problem for a company. We describe the surplus process of the company by a diffusion model with regime switching. The aim of the company is to choose a dividend policy to maximize the expected…
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…
We study decision timing problems on finite horizon with Poissonian information arrivals. In our model, a decision maker wishes to optimally time her action in order to maximize her expected reward. The reward depends on an unobservable…
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be…
This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a…
We present a novel penalty approach for a class of quasi-variational inequalities (QVIs) involving monotone systems and interconnected obstacles. We show that for any given positive switching cost, the solutions of the penalized equations…
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is…
This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random…
We consider a problem of stochastic optimal control with separable drift uncertainty in strong formulation on a finite horizon. The drift coefficient of the state $Y^{u}$ is multiplicatively influenced by an unknown random variable…