相关论文: Variance Optimal Hedging for discrete time process…

We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by F\"ollmer, Schied (2002). The…

This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…

In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a tractable formula for the expected squared hedging error…

When stochastic control problems do not possess separability and/or monotonicity, the dynamic programming pioneered by Bellman in 1950s fails to work as a time-decomposition solution method. Such cases have posted a great challenge to the…

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results…

We investigate the problem of pricing and hedging derivatives of Electricity Futures contract when the underlying asset is not available. We propose to use a cross hedging strategy based on the Futures contract covering the larger delivery…

Electricity market operators worldwide use mixed-integer linear programming to solve the allocation problem in wholesale electricity markets. Prices are typically determined based on the duals of relaxed versions of this optimization…

Recently, the volatility associated with marginal prices has increased due to large scale integration of renewable generation. Price volatility is undesirable from a consumer perspective. To address this issue, we present a framework for…

We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…

We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…

In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy},…

We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of…

Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…

This paper applies Benders decomposition to two-stage stochastic problems for energy planning under climate uncertainty, a key problem for the design of renewable energy systems. To improve performance, we adapt various refinements for…

This study deals with the pricing and hedging of single-tranche collateralized debt obligations (STCDOs). We specify an affine two-factor model in which a catastrophic risk component is incorporated. Apart from being analytically tractable,…

We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient…

It is well known that the minimal superhedging price of a contingent claim is too high for practical use. In a continuous-time model uncertainty framework, we consider a relaxed hedging criterion based on acceptable shortfall risks.…

We consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him…