Related papers: Conditional Expectation expression in mean-field S…
Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximations using jump processes that are time-homogeneous Markov,…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
We investigate the pricing of cliquet options in a jump-diffusion model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a drifted L\'{e}vy process entailing a Brownian diffusion…
The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations. We study well-posedness of the particle system as well as of its mean-field limit.…
In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston…
In this paper we obtain results for the existence and uniqueness of solutions to coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps defined on a random environment. This environment corresponds to a…
In this paper we present a new methodology for option pricing. The main idea consists to represent a generic probability distribution function (PDF) via a perturbative expansion around a given, simpler, PDF (typically a gaussian function)…
The present article studies geometric step options in exponential L\'evy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and…
Estimating nested expectations is an important task in computational mathematics and statistics. In this paper we propose a new Monte Carlo method using post-stratification to estimate nested expectations efficiently without taking samples…
In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of…
In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually…
Computing sample means on Riemannian manifolds is typically computationally costly as exemplified by computation of the Fr\'echet mean which often requires finding minimizing geodesics to each data point for each step of an iterative…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
There is recent interest in finding a potential formulation for Stochastic Partial Differential Equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single…
The mean objective of this paper is to derive an explicit formula for a price of an European option associated to the underlying delayed stock price which follows a linear differential equation with a general delay in the drift term. We use…
Conditional Asian options are recent market innovations, which offer cheaper and long-dated alternatives to regular Asian options. In contrast with payoffs from regular Asian options which are based on average asset prices, the payoffs from…
In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness…
In this work we consider the task of constructing prediction intervals in an inductive batch setting. We present a discriminative learning framework which optimizes the expected error rate under a budget constraint on the interval sizes.…