Related papers: Self-Financing Trading and the Ito-Doeblin Lemma
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…
We study the two-agent single-item bilateral trade. Ideally, the trade should happen whenever the buyer's value for the item exceeds the seller's cost. However, the classical result of Myerson and Satterthwaite showed that no mechanism can…
In this note we review the basic mathematical ideas used in finance in the language of modern physics. We focus on discrete time formalism, derive path integral and Green's function formulas for pricing. We also discuss various risk…
The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This article studies the concept in an extended formulation of the problem and…
The continuous-time version of Kyle's (1985) model is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected profits. This has…
Algorithmic stock trading has become a staple in today's financial market, the majority of trades being now fully automated. Deep Reinforcement Learning (DRL) agents proved to be to a force to be reckon with in many complex games like Chess…
This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin…
Since they were authorized by the U.S. Security and Exchange Commission in 1998, electronic exchanges have boomed, and by 2010 high frequency trading accounted for over 70% of equity trades in the US. Such markets are thought to increase…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta…
In this paper, our objective is to develop a multi-agent financial system that incorporates simulated trading, a technique extensively utilized by financial professionals. While current LLM-based agent models demonstrate competitive…
Recent developments in deep learning techniques have motivated intensive research in machine learning-aided stock trading strategies. However, since the financial market has a highly non-stationary nature hindering the application of…
In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an…
Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products…
We give an infinitesimal meaning to the symbol $dX_t$ for a continuous semimartingale $X$ at an instant in time $t$. We define a vector space structure on the space of differentials at time $t$ and deduce key properties consistent with the…
The objective of this paper is to provide a comprehensive study no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as…
We show that infinite divisibility of a trading commodity leads to a self-sustained price bubble when traders use adaptive investment strategies. The adaptive strategy can be viewed as a psychological response of a trader to the situation…
Foundation models - already transformative in domains such as natural language processing - are now starting to emerge for time-series tasks in finance. While these pretrained architectures promise versatile predictive signals, little is…
We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite showed that even…
In this paper the multivariate fractional trading ansatz of money management from Ralph Vince (Portfolio Management Formulas: Mathematical Trading Methods for the Futures, Options, and Stock Markets, John Wiley & Sons, Inc., 1990) is…