Related papers: A free boundary problem arising from a multi-state…
A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely applied investment strategy in the financial industry. Recently, Ekstr\"om, Lindberg and Tysk studied the problem of…
This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity…
We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…
In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but…
This paper studies four trading algorithms of a professional trader at a multilateral trading facility, observing a realistic two-sided limit order book whose dynamics are driven by the order book events. The identity of the trader can be…
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more…
A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is $C^1$ and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the…
In this paper we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic…
We consider a free boundary problem for the $p$-Laplace operator which is related to the so-called Bernoulli free boundary problem. In this formulation, the classical boundary gradient condition is replaced by a condition on the distance…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. In previous papers, we have established well-posedness of this problem and…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
A free boundary problem arising from the optimal reinforcement of a membrane or from the reduction of traffic congestion is considered; it is of the form $$\sup_{\int_D\theta\,dx=m}\ \inf_{u\in H^1_0(D)}\int_D\Big(\frac{1+\theta}{2}|\nabla…
The main result of this paper concerns the behavior of a free boundary arising from a minimization problem, close to the fixed boundary in two dimensions.
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…
In this paper, we study a nonlinear free boundary problem modeling the growth of spherically symmetric tumors. The tumor consists of a central necrotic core, an intermediate annual quiescent-cell layer, and an outer proliferating-cell…
We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating…
We study the existence and multiplicity of solutions of the following free boundary problem $$ (P)\left\{ \begin{array}{rcll} \del u &=& \lam ( \eps +(1-\eps ) H(u-\mu))~ \hspace{3mm}&\text{in}~\Omega (t)\\ u&=&…
Market participants regularly send bid and ask quotes to exchange-operated limit order books. This creates an optimization challenge where their potential profit is determined by their quoted price and how often their orders are…
Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…