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In this work, we consider the optimal portfolio selection problem under hard constraints on trading volume amounts when the dynamics of the risky asset returns are governed by a discrete-time approximation of the Markov-modulated geometric…
This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang,…
We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…
In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…
This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple time horizons, or when the time horizon is not known in…
Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider…
We study a stochastic control approach to managed futures portfolios. Building on the Schwartz 97 stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
We study a discounted singular stochastic control problem driven by a general L\'evy process, where the objective is to minimize a cost functional composed of a running cost and a control cost that depends on the current state of the…
This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space $\R^N$. In this article…
We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking…
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated…
The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a…
In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the…
In this paper, we study an optimal dividend and capital-injection problem in a Cram\'er--Lundberg model where claim arrivals follow a Hawkes process, capturing clustering effects often observed in insurance portfolios. We establish key…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor…