A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order for the theory to be self-consistent. The replicating methods in existing finance …
A new method in finance without probabilities or integrals.
Researchers find a timing error in Black-Scholes-Merton option pricing model.
A new approach to continuous-time universal portfolios using pathwise Itô calculus.
Naive investors make riskier choices than optimal strategies in continuous-time finance.
A new method for portfolio allocation in continuous-time markets.
We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al., and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.
Develops a mathematical model for CLMM dynamics in DeFi.
Integrates ESG factors into Bachelier's model for asset pricing.
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. SGDCT performs…
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. The parameter …
The paper calculates extreme measures in continuous time conic finance.
Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are s…
High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic …
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a path…
We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be…
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this work we consider HMMs in continuous time with both constant and switching volati…
We study financial distributions within the framework of the continuous time random walk (CTRW). We review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non-Markovian formulation of the CTRW aimed to account for correlated increme…
Deep learning solves and estimates complex financial models.
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typi…
We apply the Continuous Time Random Walk (CTRW) framework, introduced in finance by Scalas et al., to the analysis of the probability distribution of time intervals between two consecutive trades in the case of BTP futures prices traded at LIFFE in 1997. Results corroborate the validity of the CTRW approach for the des…
Quantum computing speeds up analysis of financial stochastic processes.
In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge and the option pricing partial differential equation. Approximately reversible tr…
We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can dep…
Unified treatment of CLTs for Lévy models across physics, finance, and econometrics.
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous structure as the Black-Scholes model, the widely popular option pricing model in stochas…
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predi…
ARTEMIS combines deep learning and symbolic reasoning for financial predictions.
We propose a continuous-time stock-flow consistent model for inventory dynamics in an economy with firms, banks, and households. On the supply side, firms decide on production based on adaptive expectations for sales demand and a desired level of inventories. On the demand side, investment is determined as a function o…
Paper optimizes liquidity provision in decentralized finance markets.
New method optimizes SDE models using continuous-time gradient descent.
In this paper, the relevance of the Feller conditions in discrete time macro-finance term structure models is investigated. The Feller conditions are usually imposed on a continuous time multivariate square root process to ensure that the roots have nonnegative arguments. For a discrete time approximate model, the Fell…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. …
Study on markets with insiders receiving private signals affecting asset prices and information flow.
We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtratio…
In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore i…
New methods solve complex financial equations.
S2P2 model improves predictive likelihoods for MTPPs.
We study the volatility of the MIB30-stock-index high-frequency data from November 28, 1994 through September 15, 1995. Our aim is to empirically characterize the volatility random walk in the framework of continuous-time finance. To this end, we compute the index volatility by means of the log-return standard deviatio…
SCOTCH learns system structure from irregular time series using neural SDEs.
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and time-de…
NeuralChaos efficiently approximates complex stochastic processes.
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimalit…
Study growth of LP wealth in G3Ms affected by trading fees and arbitrage.
The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of …
The paper examines non-Gaussian models for financial data.