arXiv subjects

Ju-Yi Yen

Publications and source records attributed to Ju-Yi Yen.

7 recordsLinked to original sources

arXiv2026

On the excision of Brownian bridge paths

Path transformations are fundamental to the study of Brownian motion and related stochastic processes, offering elegant constructions of the Brownian bridge, meander, and excursion. Central to this theory is the well-established link between Brownian motion and the $3$-dimensional Bessel process ${\rm BES}(3)$. This paper is specifically motivated by Pitman and Yor (2003), who showed that a ${\rm BES}(3)$ process can be constructed by excising the excursions of a Brownian path below its past maximum that reach zero and concatenating the remaining excursions. Our main result shows that a similar excision procedure, when applied to a Brownian bridge, can be related to a $3$-dimensional Bessel bridge.

math.PR↗

arXiv2025

Theoretical analysis of phase-rectified signal averaging (PRSA) algorithm

Phase-rectified signal averaging (PRSA) is a widely used algorithm to analyze nonstationary biomedical time series. The method operates by identifying hinge points in the time series according to prescribed rules, extracting segments centered at these points (with overlap permitted), and then averaging the segments. The resulting output is intended to capture the underlying quasi-oscillatory pattern of the signal, which can subsequently serve as input for further scientific analysis. However, a theoretical analysis of PRSA is lacking. In this paper, we investigate PRSA under two settings. First, when the input consists of a superposition of two oscillatory components, $\cos(2πt)+A\cos(2π(ξt+ϕ))$, where $A>0$, $ξ\in (0,1)$ and $ϕ\in [0,1)$, we show that, asymptotically when the sample size $n\to \infty$, the PRSA output takes the form $A'\sin(2πt)+B'\sin(2πξt)$, where $A',B'\neq 0$. Second, when the input is a stationary Gaussian random process, we establish a central limit theorem: under mild regularity conditions, the averaged vector produced by PRSA converges in distribution to a Gaussian random vector as $n\to \infty$ with mean determined by the covariance structure of the random process. These results indicate that caution is warranted when interpreting PRSA outputs for scientific applications.

math.ST↗

arXiv2024

An arbitrage driven price dynamics of Automated Market Makers in the presence of fees

We present a model for price dynamics in the Automated Market Makers (AMM) setting. Within this framework, we propose a reference market price following a geometric Brownian motion. The AMM price is constrained by upper and lower bounds, determined by constant multiplications of the reference price. Through the utilization of local times and excursion-theoretic approaches, we derive several analytical results, including its time-changed representation and limiting behavior.

q-fin.MF↗

arXiv2019

Detailed study of a moving average trading rule

We present a detailed study of the performance of a trading rule that uses moving average of past returns to predict future returns on stock indexes. Our main goal is to link performance and the stochastic process of the traded asset. Our study reports short, medium and long term effects by looking at the Sharpe ratio (SR). We calculate the Sharpe ratio of our trading rule as a function of the probability distribution function of the underlying traded asset and compare it with data. We show that if the performance is mainly due to presence of autocorrelation in the returns of the traded assets, the SR as a function of the portfolio formation period (look-back) is very different from performance due to the drift (average return). The SR shows that for look-back periods of a few months the investor is more likely to tap into autocorrelation. However, for look-back larger than few months, the drift of the asset becomes progressively more important. Finally, our empirical work reports a new long-term effect, namely oscillation of the SR and propose a non-stationary model to account for such oscillations.

q-fin.ST↗

arXiv2014

Information ratio analysis of momentum strategies

In the past 20 years, momentum or trend following strategies have become an established part of the investor toolbox. We introduce a new way of analyzing momentum strategies by looking at the information ratio (IR, average return divided by standard deviation). We calculate the theoretical IR of a momentum strategy, and show that if momentum is mainly due to the positive autocorrelation in returns, IR as a function of the portfolio formation period (look-back) is very different from momentum due to the drift (average return). The IR shows that for look-back periods of a few months, the investor is more likely to tap into autocorrelation. However, for look-back periods closer to 1 year, the investor is more likely to tap into the drift. We compare the historical data to the theoretical IR by constructing stationary periods. The empirical study finds that there are periods/regimes where the autocorrelation is more important than the drift in explaining the IR (particularly pre-1975) and others where the drift is more important (mostly after 1975). We conclude our study by applying our momentum strategy to 100 plus years of the Dow-Jones Industrial Average. We report damped oscillations on the IR for look-back periods of several years and model such oscilations as a reversal to the mean growth rate.

q-fin.ST↗

arXiv2008

Measuring the "non-stopping timeness" of ends of previsible sets

In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.

math.PR↗

arXiv2008

Call option prices based on Bessel processes

As a complement to some recent work by Pal and Protter, "Strict local martingales, bubbles, and no early exercise", we show that the call option prices associated with the Bessel strict local martingales are integrable over time, and we discuss the probability densities obtained thus.

math.PR↗