arXiv research

New proof shows existence of maximal surfaces with special singularities.

We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.

No arbitrage holds if a Pareto solution exists for vector-valued utility maximization.

Study robust utility maximization with uncertain continuous semimartingales.

The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…

Study robust utility maximization with uncertain endowments.

Optimal strategies found for investors in markets with transaction costs.

The study finds that maximizing median returns is the only viable strategy in portfolio selection.

This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility function $U$ is considered, with domain of definition $\mathbb{R}$. Simple conditio…

No global solutions found for time-like minimal submanifolds in Minkowski space.

We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability conditions are needed as nonexistence may arise even if the value fu…

We consider the (n-1)-plurisubharmonic flow, suggested by Tosatti-Weinkove, and prove a formula for its maximal time of existence. This includes estimates that will be useful in further investigating the flow.

Anisotropic curvature flow of networks shows unique solutions and behavior under finite time.

We prove the existence of a unique maximal surface in each anti-de Sitter (AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (that is, with conical singularities along time-like lines) for cone angles less than $π$. We interpret this result in terms of Teichmüller theory, and prove the existence of …

New method proves utility maximization without dual problem, simplifying existing results.

We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of a the Lorentz boundary manifold.

We establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility-maximization in incomplete semimartingale-driven financial markets. Unlike in the lower- and upper-hedging problems, and somewhat unexpectedly, a facelift turns out to…

Study inverse mean curvature flow on non-compact hypersurfaces, proving long-term existence and characterizing maximal time.

Study proves a criterion for curve diffusion flow blow-up.

Study robust optimization in financial markets with transaction costs.

Maximal measurable cocycles of complex hyperbolic lattices are cohomologous to representations.

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility maximization problems including the classical one…

Gradient flows for knot energies ensure long-term existence of knotted loops.

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical one…

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.

Solves Einstein vacuum equations with specific boundary conditions.

Investor optimizes worst case exponential utility in uncertain markets with unbounded endowments.

The paper studies a flow on almost complex manifolds using Chern-Ricci form.

Paper finds space-like maximal surfaces with entire null lines in 3D space-time.

In a continuous-time model with multiple assets described by càdlàg processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality bet…

In this paper we investigate a new class of growth rate maximization problems based on impulse control strategies such that the average number of trades per time unit does not exceed a fixed level. Moreover, we include proportional transaction costs to make the portfolio problem more realistic. We provide a Verificatio…

New algorithms solve linear bandits in high dimensions efficiently.

LITE efficiently estimates Gaussian PoM with linear time and memory complexity.

This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a sh…

Kähler-Einstein metrics found on compactifications of groups.

The paper uses transfinite induction to prove existence in analysis.

Model for dynamic pricing across multiple RE groups to maximize revenue.

This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously in time and are modeled as locally-bounded semi-martingales. Using a general util…

Let $(M^n, g)$ be a compact $n$-dim ($n\geq 2$) manifold with nonnegative Ricci curvature, and if $n\geq 3$ we assume that $(M^n, g)\times \mathbb{R}$ has nonnegative isotropic curvature. The lower bound of the Ricci flow's existence time on $(M^n, g)$ is proved. This provides an alternative proof for the uniform lower…

We consider the initial value problem $u_t = Δ\log u$, $u(x,0) = u_0(x)\ge 0$ in $\R^2$, corresponding to the Ricci flow, namely conformal evolution of the metric $u (dx_1^2 + dx_2^2)$ by Ricci curvature. It is well known that the maximal (complete) solution $u$ vanishes identically after time $T= \frac 1{4π} \int_{\R^…

Study examines insider information's impact on arbitrage and utility maximization in financial portfolios.

Paper solves a complex portfolio selection problem with time-inconsistent preferences.

Study on maximal surfaces with high genus in Lorentz-Minkowski space.

Optimal intervention in economic networks modeled as influence maximization, with hard computational problems.

Paper finds efficient algorithms for computing fixed points in financial networks.

Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.

Existence criteria for Chern-Ricci flows on noncompact manifolds established.

Paper develops duality theory for robust utility maximization in continuous time.