Related papers: Relative arbitrage problem under eigenvalue lower …
We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
An optimal control problem is considered for a stochastic differential equation with the cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for short). This kind of cost functional can cover the general…
In this paper, we consider a continuous-time mean-variance portfolio selection with regime-switching and random horizon. Unlike previous works, the dynamic of assets are described by non-Markovian regime-switching models in the sense that…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic…
The recent work by Cvitani\'c, Possama\"i, and Touzi (2018) [9] presents a general approach for continuous-time principal-agent problems, through dynamic programming and second-order backward stochastic differential equations (BSDEs). In…
In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and…
We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal…
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly…
We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
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…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. We first propose a general problem formulation aimed at finding a portfolio of underlying component assets by…
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the…
In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through…
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to…