相关论文: Homogenization and asymptotics for small transacti…

We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random…

We consider a robust asymptotic growth problem under model uncertainty in the presence of stochastic factors. We fix two inputs representing the instantaneous covariance for the asset price process $X$, which depends on an additional…

An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the…

This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…

We calculate asymptotic expansions for the moments of number of comparisons used by the randomized quick sort algorithm using the singularity analysis of certain generating functions.

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes…

In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which…

Using elementary arguments, we show how to derive $\mathbf{L}_p$-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities with bounded risk aversion, these estimates…

We investigate the existence of solutions of reversible and irreversible port-Hamiltonian systems. To this end, we utilize the associated exergy, a function that is composed of the system's Hamiltonian and entropy, to prove global existence…

We consider mean field game systems in time-horizon $(0,T)$, where the individual cost functional depends locally on the density distribution of the agents, and the Hamiltonian is locally uniformly convex. We show that, even if the coupling…

Taking insight from the theory of general relativity, where space and time are treated on the same footing, we develop a novel geometric variational discretization for second order initial value problems (IVPs). By discretizing the dynamics…

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…

In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while…

We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on…

The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal…

We study the homogenization of a $G$-equation which is advected by a divergence free stationary vector field in a general ergodic random environment. We prove that the averaged equation is an anisotropic deterministic G-equation and we give…

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…

We study the asymptotic behavior of solutions to linear-quadratic mean field stochastic optimal control problems. By formulating an ergodic control framework, we characterize the convergence between the finite time horizon control problem…

This paper investigates Merton's portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has a non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve…

We investigate the average minimum cost of a bipartite matching between two samples of n independent random points uniformly distributed on a unit cube in d $\ge$ 3 dimensions, where the matching cost between two points is given by any…