Related papers: Contraction options and optimal multiple-stopping …
We derive the explicit price of the perpetual American put option cancelled at the last passage time of the underlying above some fixed level. We assume the asset process is governed by a geometric spectrally negative L\'evy process. We…
This paper studies a general L\'evy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in…
Given a spectrally negative L\'evy process, we predict, in a $L_1$ sense, the last passage time of the process below zero before an independent exponential time. This optimal prediction problem generalises Baurdoux and Pedraza (2020) where…
We consider the multi-refraction strategies in two equivalent versions of the optimal dividend problem in the dual (spectrally positive L\'evy) model. The first problem is a variant of the bail-out case where both dividend payments and…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
A new approach to solve the continuous-time stochastic inventory problem using the fluctuation theory of Levy processes is developed. This approach involves the recent developments of the scale function that is capable of expressing many…
In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed…
Two-stage optimization with recourse model is an important and widely used model, which has been studied extensively these years. In this article, we will look at a new variant of it, called the two-stage optimization with recourse and…
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…
We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by…
In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not…
We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a…
We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish…
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…
In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions rather than an RCLL process. We…
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved…
We revisit an absolutely-continuous version of the stochastic control problem driven by a L\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex.…
In the literature on optimal stopping, the problem of maximizing the expected discounted reward over all stopping times has been explicitly solved for some special reward functions (including $(x^+)^{\nu}$, $(e^x-K)^+$, $(K-e^{-x})^+$,…
This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to…