Related papers: A free boundary problem arising from a multi-state…
We study a mathematical model motivated by the support/resistance line method in technical analysis where the underlying stock price transitions between three states of nature in a path-dependent manner. For optimal stopping problems with…
This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule…
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…
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…
Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries…
This paper studies an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by…
In this paper, we undertake an investigation into the utility maximization problem faced by an economic agent who possesses the option to switch jobs, within a scenario featuring the presence of a mandatory retirement date. The agent needs…
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…
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of…
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…
This paper studies the parabolic free boundary problem arising from pricing American-style put options on an asset whose index follows a geometric Brownian motion process. The contribution is to propose a condition for that the early…
Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
We consider Merton's problem with proportional transaction costs. It is well known that the optimal investment strategy is characterized by two trading boundaries, the buy boundary and the sell boundary, between which lies the no-trading…
In this paper we investigate a new class of growth rate maximization problems based on impulse control strategies such that the average number of trades per time unit does not exceed a fixed level. Moreover, we include proportional…
We study the higher regularity of free boundaries in obstacle problems for integro-differential operators. Our main result establishes that, once free boundaries are $C^{1,\alpha}$, then they are $C^\infty$. This completes the study of…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
We consider the free boundary problem arising from an energy functional which is the sum of a Dirichlet energy and a nonlinear function of either the classical or the fractional perimeter. The main difference with the existing literature is…
In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…
We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogeneously, our analysis is two-fold: we study the regularity of the solutions and some geometric…