相关论文: Viscosity Characterization of the Arbitrage Functi…
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes…
We study the problem of utility maximization from terminal wealth in which an agent optimally builds her portfolio by investing in a bond and a risky asset. The asset price dynamics follow a diffusion process with regime-switching…
This paper is devoted to solving a class of second order Hamilton-Jacobi-Bellman (HJB) equations in the Wasserstein space, associated with mean field control problems involving common noise. The well-posedness of viscosity solutions to the…
The paper deals with a Bolza optimal control problem for a dynamical system which motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional in this…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order $\alpha \in (0, 1)$ and a Bolza cost functional. The differential game is associated to the…
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be traded continuously, while the…
We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper.…
In this work we investigate regularity properties of a large class of Hamilton-Jacobi-Bellman (HJB) equations with or without obstacles, which can be stochastically interpreted in form of a stochastic control system which nonlinear cost…
We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the…
In this paper, we study optimal liquidation problems in a randomly-terminated horizon. We consider the liquidation of a large single-asset portfolio with the aim of minimizing a combination of volatility risk and transaction costs arising…
In this paper we investigate a Principal-Agent problem with moral hazard under Knightian uncertainty. We extend the seminal framework of Holmstr\"om and Milgrom by combining a Stackelberg equilibrium with a worst-case approach. We…
This paper studies the problem of optimally extracting nonrenewable natural resource in light of various financial and economic restrictions and constraints. Taking into account the fact that the market values of the main natural resources…
In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second…
The aim of this paper is to introduce an insurance model allowing reinsurance and dividend payment. Our model deals with several homogeneous contracts and takes into account the legislation regarding the provisions to be justified by the…
The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a transport equation with boundary control. A suitable viscosity solution approach is needed in view of the…
A suitable notion of weak solution to infinite-dimensional rate-independent systems, called Inertial Balanced Viscosity (IBV) solution, is introduced. The key feature of such notion is that the energy dissipated at jump discontinuities…
Motivated by parallels between mean field games and random matrix theory, we develop stochastic optimal control problems and viscosity solutions to Hamilton-Jacobi equations in the setting of non-commutative variables. Rather than real…
We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. We allow for general…
This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique existence theorem of the solution for initial value problems.…