Related papers: An Exact Connection between two Solvable SDEs and …
This paper deals with the backward Euler method applied to semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. The SPDE is discretized in space by the finite element method and in time by the…
Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger equation, $r_{n}(E)$, which are monotonic functions of the energy, determine a unique potential when the domain of the…
We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to…
The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem, in this work we will be concerned with the nonlinear…
We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function we adopt a g-expectation. In contrast to the standard framework of financial engineering,…
Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and…
We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local)…
In this paper we consider a mean-field backward stochastic differential equation (BSDE) driven by a Brownian motion and an independent Poisson random measure. Translating the splitting method introduced by Buckdahn, Li, Peng and Rainer [6]…
We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the…
Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of…
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly…
For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price…
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…
Minimax optimization problems have attracted a lot of attention over the past few years, with applications ranging from economics to machine learning. While advanced optimization methods exist for such problems, characterizing their…
We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and R\'{a}sonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to…
Let $(X_t)_{t \ge 0}$ be the solution of the stochastic differential equation $$dX_t = b(X_t) dt+A dZ_t, \quad X_{0}=x,$$ where $b: \mathbb{R}^d \rightarrow \mathbb R^d$ is a Lipschitz function, $A \in \mathbb R^{d \times d}$ is a positive…
We study the invariant measures of infinite systems of stochastic differential equations (SDEs) indexed by the vertices of a regular tree. These invariant measures correspond to Gibbs measures associated with certain continuous…
In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or…
This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by…
The classical Merton investment problem predicts deterministic, state-dependent portfolio rules; however, laboratory and field evidence suggests that individuals often prefer randomized decisions leading to stochastic and noisy choices.…