Related papers: BSDEs under partial information and financial appl…
With an emphasis on generators with quadratic growth in the control variable we consider measure solutions of BSDE, a solution concept corresponding to the notion of risk neutral measure in mathematical finance. In terms of measure…
We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual…
In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with sub-differential operators that are driven by infinite-dimensional martingales which involve symmetry, that is, the process involves a positive…
This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and…
This paper is devoted to proposing a new asymmetric risk-sensitive criterion involving different risk attitudes toward varying risk sources. The criterion can only be defined through the initial value of the minimal solutions of quadratic…
We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models,…
In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and…
We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio process converges to the solution of an…
We construct planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-Shepp-type equations and a change-of-variable formula in the spirit of Freidlin-Sheu for these so-called "Walsh…
We apply the theory of McKean-Vlasov-type SDEs to study several problems related to market efficiency in the context of partial information and partially observable financial markets: (i) convergence of reduced-information market price…
This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial…
We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show…
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…
The semimartingale stochastic approximation procedure, namely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation…
Using properties of backward stochastic differential equations we give new proofs of some well known results on BMO martingales and improve some estimates of BMO norms.
We study partial information Nash equilibrium between a broker and an informed trader. In this setting, the informed trader, who possesses knowledge of a trading signal, trades multiple assets with the broker in a dealer market.…
In this paper we formulate and study an optimal switching problem under partial information. In our model the agent/manager/investor attempts to maximize the expected reward by switching between different states/investments. However, he is…
This paper presents the integral(or differential) form of G-BSDEs, gives some kind of apriori estimates of their solutions, and under a very strong condition, proves the G-martingale representation theorem, and the existence and uniqueness…
In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness…
We introduce a generalized notion of semilinear elliptic partial differential equations where the corresponding second order partial differential operator $L$ has a generalized drift. We investigate existence and uniqueness of generalized…