arXiv research

Logarithmic regret for continuous-time reinforcement learning.

We have studied the statistical mechanics of money circulation in a closed economic system. An explicit statistical formulation of the circulation velocity of money is presented for the first time by introducing the concept of holding time of money. The result indicates that the velocity is governed by behavior pattern…

Study on Bitcoin transaction flows and holding times, revealing multifractal and power-law distributions.

We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. Th…

Study schedules jobs with unknown holding costs to minimize expected cumulative cost.

Study how transaction costs impact stock returns and holdings in equilibrium.

This thesis examines the accuracy of scaling VaR estimates for longer holding periods.

Paper develops a continuous-time framework for financial markets without stochastic calculus.

Let ${\bf M}$ be a compact Riemannian manifold and the metrics $g=g(t)$ evolve by the Ricci flow. We prove the following result. The Sobolev imbedding by Aubin or Hebey, perturbed by a scalar curvature term and modulo sharpness of constants, holds uniformly for $({\bf M}, g(t))$ for all time if the Ricci flow exists fo…

Study finds stock selection ability of Chinese mutual funds is better than asset allocation ability.

The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution c…

For the stochastic multi-armed bandit (MAB) problem from a constrained model that generalizes the classical one, we show that an asymptotic optimality is achievable by a simple strategy extended from the $ε_t$-greedy strategy. We provide a finite-time lower bound on the probability of correct selection of an optimal ne…

Symplectic manifold rays can be removed without changing the manifold's structure.

The determinants of the velocity of money have been examined based on life-cycle hypothesis. The velocity of money can be expressed by reciprocal of the average value of holding time which is defined as interval between participating exchanges for one unit of money. This expression indicates that the velocity is govern…

Study examines stock price correlations between Indonesian holding companies and their subsidiaries.

We find that factors explaining bank loan recovery rates vary depending on the state of the economic cycle. Our modeling approach incorporates a two-state Markov switching mechanism as a proxy for the latent credit cycle, helping to explain differences in observed recovery rates over time. We are able to demonstrate ho…

In practice daily volatility of portfolio returns is transformed to longer holding periods by multiplying by the square-root of time which assumes that returns are not serially correlated. Under this assumption this procedure of scaling can also be applied to contributions to volatility of the assets in the portfolio. …

Let $\{u_n\}$ be a sequence of maps from a compact Riemann surface $M$ with smooth boundary to a general compact Riemannian manifold $N$ with free boundary on a smooth submanifold $K\subset N$ satisfying \[ \sup_n \ \left(\|\nabla u_n\|_{L^2(M)}+\|τ(u_n)\|_{L^2(M)}\right)\leq Λ, \] where $τ(u_n)$ is the tension field o…

Mean field game with defaultable agents and systemic risk quantified.

If $G$ is a compact Lie group endowed with a left invariant metric $g$, then $G$ acts via pullback by isometries on each eigenspace of the associated Laplace operator $Δ_g$. We establish algebraic criteria for the existence of left invariant metrics $g$ on $G$ such that each eigenspace of $Δ_g$, regarded as the real ve…

Global solutions and smoothing effects for reaction-diffusion equations on manifolds.

It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper addresses the question of whether an alternative model for stock price exists for…

Kyle's equilibrium model stability proven for 1-2 trading times, but not for 3 or more.

Continuous-time model shows insider trading constraints impact market dynamics.

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal …

The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using $Φ$-divergence.

Constant and symmetric price impact functions, most commonly used in agent-based market modelling, are shown to give rise to paradoxical and inconsistent outcomes in the simplest case of arbitrage exploitation when open-hold-close actions are considered. The solution of the paradox lies in the non-constant nature of re…

We study the statistical properties of the iterates generated by gradient descent, applied to the fundamental problem of least squares regression. We take a continuous-time view, i.e., consider infinitesimal step sizes in gradient descent, in which case the iterates form a trajectory called gradient flow. Our primary f…

This paper studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset's payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories and trading rates. The un…

The firefighter game problem on locally finite connected graphs was introduced by Bert Hartnell. The game on a graph $G$ can be described as follows: let $f_n$ be a sequence of positive integers; an initial fire starts at a finite set of vertices; at each (integer) time $n\geq 1$, $f_n$ vertices which are not on fire b…

Representative investors whose behaviour is modelled by a deterministic finite automaton generate complexity both in the time series of each asset and in the cross-sectional correlation when the rule governing their behaviour is schizophrenic, meaning the investor must hold multiple seemingly contradictory beliefs simu…

Sharp inequalities for matrix means with unknown variance.

On a polarized manifold $(X,L)$, the Bergman iteration $φ_k^{(m)}$ is defined as a sequence of Bergman metrics on $L$ with two integer parameters $k, m$. We study the relation between the Kähler-Ricci flow $φ_t$ at any time $t \geq 0$ and the limiting behavior of metrics $φ_k^{(m)}$ when $m=m(k)$ and the ratio $m/k$ ap…

We propose confidence sequences -- sequences of confidence intervals which are valid uniformly over time -- for quantiles of any distribution over a complete, fully-ordered set, based on a stream of i.i.d. observations. We give methods both for tracking a fixed quantile and for tracking all quantiles simultaneously. Sp…

We have studied numerically the statistical mechanics of the dynamic phenomena, including money circulation and economic mobility, in some transfer models. The models on which our investigations were performed are the basic model proposed by A. Dragulescu and V. Yakovenko [1], the model with uniform saving rate develop…

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the continuous diffusion process associated with the algorithm converges exponentially fa…

In this research we study a finite horizon optimal purchasing problem for items with a mean reverting price process. Under this model a fixed amount of identical items are bought under a given deadline, with the objective of minimizing the cost of their purchasing price and associated holding cost. We prove that the op…

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show t…

Unified framework for anytime-valid PAC-Bayes bounds.

Study examines how bank holding structures affect financial stress spread.

In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product $P_1\times P_2$ of two strongly geometrically bounded symplectic manifolds under some conditions with $P_1$. In particular, if $N$ is a closed manifold or a noncompact manifold of finite topological type, our result…

This research evaluates measures of dependence for financial time-series data.

In this article, we study complete surfaces $Σ$, isometrically immersed in the product space $\mathbb{H}^2\times\mathbb{R}$ or $\mathbb{S}^2\times\mathbb{R}$ having positive extrinsic curvature $K_e$. Let $K_i$ denote the intrinsic curvature of $Σ$. Assume that the equation $aK_i+bK_e=c$ holds for some real constants $…

The problem of resource allocation of nonlinear networked control systems is investigated, where, unlike the well discussed case of triggering for stability, the objective is optimal triggering. An approximate dynamic programming approach is developed for solving problems with fixed final times initially and then it is…

Study finds optimal boundaries for hedging a perpetual American put option.

This paper revisits optimal investment strategies for defined contribution pension schemes using forward preferences.

We derive a logarithmic Sobolev inequality along the Ricci flow without any restriction on time, which depends only on the initial metric via rudimentary geometric data, assuming only that a certain first eigenvalue is positive. As a consequence we obtain a uniform Sobolev inequality along the Ricci flow without any re…

Higher-dimensional Schwarzschild spacetimes violate the Penrose property.