Related papers: A First-Order BSPDE for Swing Option Pricing: Clas…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems…
This paper considers the asset price p as relations C=pV between the value C and the volume V of the executed transactions and studies the consequences of this definition for the option pricing equations. We show that the classical BSM…
We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…
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,…
In this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to…
This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
In this paper, we study the optimal multiple stopping problem under Knightian uncertainty both under discrete-time case and continuous-time case. The Knightian uncertainty is modeled by a single real-valued function g, which is the…
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…
This paper studies the differentiability of the value function of switched linear systems under arbitrary switching and controlled switching, referred to as worst-case and optimal value functions respectively. First, we show that the value…
Recent developments on financial markets have revealed the limits of Brownian motion pricing models when they are applied to actual markets. L\'evy processes, that admit jumps over time, have been found more useful for applications. Thus,…
A robust control problem is considered in this paper, where the controlled stochastic differential equations (SDEs) include ambiguity parameters and their coefficients satisfy non-Lipschitz continuous and non-linear growth conditions, the…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…
This paper presents a new model for options pricing. The Black-Scholes-Merton (BSM) model plays an important role in financial options pricing. However, the BSM model assumes that the risk-free interest rate, volatility, and equity premium…
We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…