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In this paper, we consider the fully coupled forward-backward stochastic functional differential equations (FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward…
This article is focused on using a new measurement of risk-- Weighted Value at Risk to develop a new method of constructing initiate from the TVAR solving problem, based on MATLAB software, using the historical simulation method (avoiding…
A coupled forward-backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier-Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the…
In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue…
This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time-dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on…
This paper studies the mean-variance optimal portfolio choice of an investor pre-committed to a deterministic investment policy in continuous time in a market with mean-reversion in the risk-free rate and the equity risk-premium. In the…
We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants…
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is…
Portfolio optimization methods suffer from a catalogue of known problems, mainly due to the facts that pair correlations of asset returns are unstable, and that extremal risk measures such as maximum drawdown are difficult to predict due to…
The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion. It gives then a method for…
We study an optimal portfolio problem designed for an agent operating in intraday electricity markets. The investor is allowed to trade in a single risky asset modelling the continuously traded power and aims to maximize the expected…
For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…
Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of…
This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete.…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic…
Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient…