Related papers: Monotonicity of the value function for a two-dimen…
We consider a real options model for the optimal irreversible investment problem of a profit maximizing company. The company has the opportunity to invest into a production plant capable of producing two products, of which the prices follow…
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…
We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…
Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a…
In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided…
We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian stochastic factor drives both of them. Moreover, we model…
We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space.…
In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov…
This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…
This paper is devoted to the synchronization of stochastic differential equations driven by the linear multiplicative fractional Brownian motion with Hurst parameter $H\in(\frac{1}{2},1)$. We firstly prove that the equation has a unique…
We study the problem of optimal inside control of a stochastic Volterra equation driven by a Brownian motion and a Poisson random measure. We prove a sufficient and a necessary maximum principle for the optimal control when the trader has…
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a…
We propose an alternative approach for solving a number of well-studied optimal stopping problems for L\'evy processes. Instead of the usual method of guess-and-verify based on martingale properties of the value function, we suggest a more…
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a…
We consider the optimal stopping problem $v^{(\eps)}:=\sup_{\tau\in\mathcal{T}_{0,T}}\mathbb{E}B_{(\tau-\eps)^+}$ posed by Shiryaev at the International Conference on Advanced Stochastic Optimization Problems organized by the Steklov…