arXiv research

Investment decisions shift earlier as patience decreases, with implications for pasting conditions.

We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through …

Study optimal stopping times for multi-dimensional processes with non-exponential discounting.

In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in [17], with optimal contracting between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian contagion. We provide here a comprehensive mathematical formulation of the model …

An ability to postpone one's execution without penalty provides an important strategic advantage in high-frequency trading. To elucidate competition between traders one has to formulate to a quantitative theory of formation of the execution price from market expectations and quotes. This theory was provided in 2005 by …

We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism used in stock markets. Both buyers and sellers are elastic in the price-quantity …

With negative growth in real production in many countries and debt levels which become an increasing burden on developed societies, the calls for a change in economic policy and even the monetary system become louder and increasingly impatient. We research the consequences of a system of credit and debt, that still all…

Investors with anxiety about drawdowns may use stop-loss and trailing stops as optimal selling strategies.

We study the market selection hypothesis in complete financial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and learning mechanism, risk aversion, impatience and 'catching up with Joneses' preferen…

We consider a power utility maximization problem with additive habits in a framework of discrete-time markets and random endowments. For certain classes of incomplete markets, we establish estimates for the optimal consumption stream in terms of the aggregate state price density, investigate the asymptotic behaviour of…

Study shows how learning and analytical models affect reneging and jockeying in a dual M/M/1 system.

Characterizes a general range decreasing group homomorphism.

We propose a method to decrease the number of hidden units of the restricted Boltzmann machine while avoiding decrease of the performance measured by the Kullback-Leibler divergence. Then, we demonstrate our algorithm by using numerical simulations.

Sharp estimate for flow in any dimension.

In this paper, we propose a novel sufficient decrease technique for stochastic variance reduced gradient descent methods such as SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new sufficient decrease criterion, which yields sufficient decrease versions of stochastic varianc…

In this paper, we propose a novel sufficient decrease technique for variance reduced stochastic gradient descent methods such as SAG, SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new sufficient decrease criterion, which yields sufficient decrease versions of variance redu…

Paper proves genus of surfaces decreases in mean curvature flow.

The paper analyzes a game where players must balance short-term and long-term interests, leading to cooperative or competitive outcomes.

GD monotonically decreases GFS sharpness in neural networks and scalar models.

Numerical observations on martingale couplings are confirmed under certain conditions.

DRAG decreases regularization to accelerate semi-discrete OT convergence.

We discuss a special class of solutions to the minimal surface system. These are vector-valued functions that "decrease area" and are natural generalization of scalar functions. After defining area-decreasing maps, we show several classical results for the minimal surface equation can be generalized. We also conjecture…

Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.

We consider the mean curvature flow of the graph of a smooth map $f:\mathbb{R}^2\to\mathbb{R}^2$ between two-dimensional Euclidean spaces. If $f$ satisfies an area-decreasing property, the solution exists for all times and the evolving submanifold stays the graph of an area-decreasing map $f_t$. Further, we prove unifo…

New SAGA algorithm with decreasing step for stochastic optimization.

New RL algorithm reduces regret in birth-death queueing problems.

New algorithm optimizes long-term user satisfaction in recommendation systems.

Study geometrically characterizes piecewise circular curves with decreasing curvature.

Improved option pricing model with transaction costs.

In this work we classify the stable regions (second order minima of perimeter under an area constraint) in tori of revolution with piecewise continuous decreasing Gauss curvature from the longest parallel and with a horizontal symmetry. Some applications to isoperimetric problems are also given.

Optimal insurance minimizes ruin probability with non-decreasing functions.

Parity calibration aims to predict increase-decrease events, not values.

We decrease the $rms$ mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately chosen non-minimal surface, we achieve up to 65 percent of the total possible decr…

Let $f:M\to N$ be a smooth area decreasing map between two Riemannian manifolds $(M,\gm)$ and $(N,\gn)$. Under weak and natural assumptions on the curvatures of $(M,\gm)$ and $(N,\gn)$, we prove that the mean curvature flow provides a smooth homotopy of $f$ to a constant map.

We present a modified version of the non parametric Hawkes kernel estimation procedure studied in arXiv:1401.0903 that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that this method allows us to estimate faithfully a power-law decreasing kernel over at…

New algorithm optimizes for long-term user satisfaction in delayed reward settings.

Maps on foliated manifolds decrease area and scalar curvature is negative.

We solve an optimal consumption problem with habit formation constraints.

In this article we give a complete description of the evolution of an area decreasing map $f:M\to N$ induced by its mean curvature in the situation where $M$ and $N$ are complete Riemann surfaces with bounded geometry, $M$ being compact, for which their sectional curvatures $σ_M$, $σ_N$ satisfy $\minσ_M\ge\supσ_N$.

The recently announced Energy Union by the European Commission is the most recent step in a series of developments aiming at integrating the EU's gas markets to increase social welfare (SW) and security of gas supply. Based on a spatial partial equilibrium model, we analyze the changes in consumption, prices, and SW up…

In this note, we show that the solution to the Dirichlet problem for the minimal surface system in any codimension is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a minimal submanifold $Σ$ is the graph of a (strictly) distance-decreasing map, then $…

Study connects curvature bounds to map existence and flow solutions.

For 3-dimensional hyperbolic cone structures with cone angles $θ$, local rigidity is known for $0 \leq θ\leq 2π$, but global rigidity is known only for $0 \leq θ\leq π$. The proof of the global rigidity by Kojima is based on the fact that hyperbolic cone structures with cone angles at most $π$ do not degenerate in defo…

Topological entropy decreases strictly along Ricci flow near hyperbolic metrics.

GradaGrad adapts learning rate non-monotonically, overcoming AdaGrad's step size decrease.

Traditional landscape analysis of deep neural networks aims to show that no sub-optimal local minima exist in some appropriate sense. From this, one may be tempted to conclude that descent algorithms which escape saddle points will reach a good local minimum. However, basic optimization theory tell us that it is also p…

Study shows adding similar investors can either increase or decrease profits, depending on their strategy.

Changing kernel bandwidth during training improves kernel regression performance.